The conditional pdfs are as follows:
fy(y|X=2)=dΦ(y-2)dyfy(y|X=−2)=dΦ(y+2)dyAnswer:fy(y|X=2)=dΦ(y−2)dyfy(y|X=−2)=dΦ(y+2)dy
Given:
A binary transmission system transmits a signal X of value -2[V] to send a "O" and 2[V] to send a "1".Let Y = X + N be the received signal, where N is a random variable with normal standard distribution that represents an additive noise.To Determine:We need to find the conditional pdfs fy(y|X = 2) and fy(y|X = -2)We know that,The standard Normal Distribution formula is given byf(x)=1/√2πe−x22f(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}f(x)=2π1e−2x2A binary transmission system transmits a signal X of value -2[V] to send a "O" and 2[V] to send a "1".Let X takes only two values +2 or -2.Therefore,P(X=+2)=P(X=-2)=0.5We need to find the conditional pdfs fy(y|X = 2) and fy(y|X = -2)We can calculate the expected values of Y,E(Y|X=2) = E(X|X=2) + E(N) = 2+0 = 2E(Y|X=-2) = E(X|X=-2) + E(N) = -2+0 = -2The conditional pdfs fy(y|X = 2) and fy(y|X = -2) are given byfy(y|X=2) = P(Y ≤ y | X = 2)fy(y|X=-2) = P(Y ≤ y | X = -2)P(Y ≤ y | X = 2) = P(X + N ≤ y | X = 2) = P(N ≤ y - X | X = 2) = ∫-∞y-2fN(x)dx∫-∞∞fN(x)dx=∫-∞y-2f(x−2)dx∫-∞∞f(x−2)dx=∫-∞y-22πe−12(x−2)2dx∫-∞∞2πe−12(x−2)2dxP(Y ≤ y | X = 2) = Φ(y-2)P(Y ≤ y | X = -2) = P(X + N ≤ y | X = -2) = P(N ≤ y + 2 | X = -2) = ∫-∞y+2fN(x)dx∫-∞∞fN(x)dx=∫-∞y+22πe−12(x+2)2dx∫-∞∞2πe−12(x+2)2dxP(Y ≤ y | X = -2) = Φ(y+2)where Φ(.) denotes the standard normal cumulative distribution function.
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The value of a binary transmission system that transmits a signal X of value -2[V] to send a "O" and 2[V] to send a "1" is called binary. A normal random variable is N that represents an additive noise in the received signal Y = X + N.
Hence, the conditional pdfs are given by:
[tex]f(y|X = 2) = \frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y-2)^{2}}{2})$[/tex]
[tex]f(y|X = -2) = \frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y+2)^{2}}{2})$[/tex]
(i) Fy(y|X = 2),
(ii) Fy(y|X = -2) are the conditional probability density functions (pdfs). The difference between "f" and "F" is that "f" represents the probability density function and "F" represents the cumulative distribution function. The conditional pdfs fy(y|X = 2),
fy(y|X = -2) can be obtained as follows:
fy(y|X = 2)
Y = 2 + N
If Y = y, then
N = y - 2.
Fy(y|X = 2) is the distribution function of N and it can be given as:
[tex]F(y|X = 2)=\int_{-\infty}^{y}\frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{n^{2}}{2})dn[/tex]
[tex]f(y|X = 2)=\frac{\partial F(y|X = 2)}{\partial y}=\frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y-2)^{2}}{2})\end{align*}$[/tex]
Similarly, fy(y|X = -2)
Y = -2 + N
If Y = y,
then N = y + 2.
Fy(y|X = -2) is the distribution function of N and it can be given as:
[tex]F(y|X = -2)=\int_{-\infty}^{y}\frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{n^{2}}{2})dn[/tex]
[tex]f(y|X = -2)=\frac{\partial F(y|X = -2)}{\partial y}=\frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y+2)^{2}}{2})\end{align*}[/tex]
Hence, the conditional pdfs are given by:
[tex]f(y|X = 2) = \frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y-2)^{2}}{2})$[/tex]
[tex]f(y|X = -2) = \frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y+2)^{2}}{2})$[/tex]
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I need help with short sides of the triangles on Pythagorean theorem
Answer:
5
Step-by-step explanation:
13² - 12² = 25
√25 = 5
Have a great day <3
Find the area of a sector with central angle 27/8 rad in a circle of radius 4 m.
The area of the sector with a central angle of 27/8 radians in a circle of radius 4 meters is 27 square meters.
To find the area of a sector, you can use the formula:
Area of Sector = (θ/2π) * πr²
where θ is the central angle in radians and r is the radius of the circle.
Given:
Central angle (θ) = 27/8 radians
Radius (r) = 4 meters
Substituting the given values into the formula, we have:
Area of Sector = (27/8 * 1/(2π)) * π * (4)^2
Simplifying the expression:
Area of Sector = (27/8 * 1/2) * (4)^2
Area of Sector = (27/16) * 16
Area of Sector = 27 square meters
Therefore, the area of the sector with a central angle of 27/8 radians in a circle of radius 4 meters is 27 square meters.
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let x equals negative 14 times pi over 3 period part a: determine the reference angle of x. (4 points) part b: find the exact values of sin x, tan x, and sec x in simplest form. (6 points)
The exact values of sin x, tan x and sec x in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.
To solve this problem, we'll work with the angle x, which is equal to -14π/3. Part a: Determine the reference angle of x. The reference angle is the positive acute angle formed between the terminal side of the angle and the x-axis. To find the reference angle, we ignore the negative sign and convert the angle to its equivalent positive angle within one revolution.
The positive equivalent angle can be obtained by adding 2π (or 360 degrees) repeatedly until we obtain a positive angle. In this case, we have: -14π/3 + 2π = -14π/3 + 6π/3 = -8π/3. The reference angle of x is 8π/3. Part b: Find the exact values of sin x, tan x, and sec x in simplest form. sin x = sin(-14π/3) = -sin(14π/3) (Using the symmetry of sine function)
= -sin(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)
= -sin(2π/3) (Sine of an angle 2π/3 is known) = -√3/2.
tan x = tan(-14π/3) = tan(14π/3) (Using the symmetry of tangent function)
= tan(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)
= tan(2π/3) (Tangent of an angle 2π/3 is known)= √3. sec x = sec(-14π/3) = sec(14π/3) (Using the symmetry of secant function)= sec(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)= sec(2π/3) (Secant of an angle 2π/3 is known)= -2/√3. Therefore, the exact values in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.
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Answer: The exact values of sin x, tan x and sec x in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.
Step-by-step explanation: To solve this problem, we'll work with the angle x, which is equal to -14π/3. Part a: Determine the reference angle of x. The reference angle is the positive acute angle formed between the terminal side of the angle and the x-axis. To find the reference angle, we ignore the negative sign and convert the angle to its equivalent positive angle within one revolution.
The positive equivalent angle can be obtained by adding 2π (or 360 degrees) repeatedly until we obtain a positive angle. In this case, we have: -14π/3 + 2π = -14π/3 + 6π/3 = -8π/3. The reference angle of x is 8π/3. Part b: Find the exact values of sin x, tan x, and sec x in simplest form. sin x = sin(-14π/3) = -sin(14π/3) (Using the symmetry of sine function)
= -sin(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)
= -sin(2π/3) (Sine of an angle 2π/3 is known) = -√3/2.
tan x = tan(-14π/3) = tan(14π/3) (Using the symmetry of tangent function)
= tan(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)
= tan(2π/3) (Tangent of an angle 2π/3 is known)= √3. sec x = sec(-14π/3) = sec(14π/3) (Using the symmetry of secant function)= sec(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)= sec(2π/3) (Secant of an angle 2π/3 is known)= -2/√3. Therefore, the exact values in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.
What is the range of the function f = [0,00) + R, defined by the rule f(t) = -247 (a) (0,1) (c) R (b) (0,11 (d) (0,00)
The range of the function f = [0,00) + R, defined by the rule f(t) = -247 is {-247}. The correct option is d.
The range of a function is the set of all possible outputs or y-values. Here, the function is f(t) = -247 with the domain [0,00), which means that for any value of t between 0 and 00 (excluding 00), the function will always give the same output, -247. This is because the rule for the function is simply -247, and doesn't depend on the input value of t.
The range of the function f is simply {-247}, which is a singleton set containing only one element (-247). In other words, the only possible output or y-value for this function is -247, and there are no other possible values for f(t) for any value of t between 0 and 00 (excluding 00).
Thus, the correct option is d.
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please help me .........
Answer: the answer is b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
first add them together. the y cancels out and your left with 3x=15. divide by 3 on both sides and you get x=5. The only answer with positive 5 as an x value is b
During the summer John collected cans to recycle. In August he collected 718 cans bringing his total to 2,275 cans. How many cans did John collect before August?
Answer: 1557 cans
Step-by-step explanation:
Since we are informed that John collected 718 cans in August bringing his total number of cans to 2,275 cans, the number of cans that John collected before August will be:
= Total number of cans collected - Number of cans collected in August
= 2275 - 718
= 1557 cans
A scalene triangle has sides measuring 200 feet, 107 feet, and 221 feet. What is the
perimeter of the triangle?
Answer:
P = 528
Step-by-step explanation:
P = a + b + c = 200 + 107 + 221 = 528
The cost to place an ad in a weekly paper is $5.50 per line,i.The print set-up fee is $7.50.
Answer:
whats the question?
Step-by-step explanation:
Software can generate samples from (almost) exactly Normal distributions.
Here is a random sample of size 5 from the Normal distribution with mean 10 and standard deviation 2:
6.47 7.51 10.10 13.63 9.91
These data match the conditions for a z test better than real data will: the population is very close to Normal and has known standard deviation s = 2, and the population mean is µ = 10.
Test the hypotheses
H0 : µ = 8
Ha : µ ? 8
In Exercise 15.41 (given above), a sample from a Normal population with mean µ = 10 and standard deviation s = 2 failed to reject the null hypothesis H0 : µ = 8 at the a = 0.05 significance level.
Enter the information from this example into the Power of a Test applet.
(Don't forget that the alternative hypothesis is two-sided.)
What is the power of the test against the alternative µ = 10?
The power of the test against the alternative µ = 10 is 1.
Given: A sample from a Normal population with mean µ = 10 and standard deviation s = 2 failed to reject the null hypothesis
H0: µ = 8 at the a = 0.05 significance level.
To find :
The power of the test against the alternative µ = 10.
Step 1: We have
H0 : µ = 8
Ha: µ ≠ 8α
= 0.05
Sample size n = 5
Population Standard deviation s = 2
Population means µ = 10
The alternative hypothesis is two-sided.
Hence α/2 = 0.025.
Using a normal table, the critical values for a two-tailed test at the 0.05 level of significance are -1.96 and +1.96 respectively.
Step 2: We know that
[tex]\[z=\frac{\overline{x}-\mu }{\frac{s}{\sqrt[]{n}}}\][/tex]
where [tex]\[\overline{x}\][/tex] = sample mean,
µ = Population mean,
s = Population Standard deviation and
n = sample size.
By using the given data, z can be calculated as below:
[tex]\[z=\frac{10-8}{\frac{2}{\sqrt[]{5}}}[/tex]
=[tex]4.47[/tex]
The value of z falls in the critical region if it is less than -1.96 or greater than +1.96.
Since 4.47 is greater than +1.96, the null hypothesis is rejected.
Since the null hypothesis is rejected, it is logical to expect that the power of the test will be high.
Hence, the power of the test against the alternative µ = 10 is 1 (100%).
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Please help if you wantbbrainleist! :(
i need to find the area and circumference for each circle
Answer:
Step-by-step explanation:
5
Quadratic Functions
Determine the value of y, if x is −9. y=x^2+8
Answer:nn
Step-by-step explanationn o:
Answer:
y = 89
Step-by-step explanation:
x = -9
y = x^2 + 8
y = (-9)^2 + 8
y = 81 + 8
y = 89
What is the name of the blue dot located inside the curve of the parabola
below?
O A. Focus
B. Center
O C. Directrix
D. Vertex
The blue dot located inside the curve of the parabola is Focus.
What are Parts in Parabola?
The essential feature of a parabola is that all of its points are the same distance from a point called the focus and a line called the directrix. The vertex, axis, latus rectum, and focal length are also key components of a parabola.
The latus rectum, also known as the focal diameter, is the line segment that runs through the focus and parallel to the directrix. The focal diameter's endpoints are located on the curve.
A parabola is the set of all points ( x, y ) in a plane that are the same distance from a fixed line called the directrix and a fixed point not on the directrix (the focus).
A parabola will have three key components: a focus, a directrix, and a vertex. This upward-opening parabola demonstrates that all points,, along the parabola's curve will be the same distance from the focus and the directrix.
Thus, the blue dot located inside the curve of the parabola is Focus.
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Which inequality is true if p = 3.4 ?
Answer:
the shape isnt angled thats what it means
Step-by-step explanation:
The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with 100 and 11. The proportion of adults with scores above 110 is closest to 0.25 b.0.33. c0.14. 4.0.18 Colleges often rely heavily on raising money for an "annual fund" to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's smal income is a good predicar of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. In the stadies described a annual income is an explanatory variable. b the correlation between annual income and the size of the donation is positive. c the size of the donation to the annual fund is the response variable. d. All of the answer options are correct.
The proportion of adults with scores above 110 is 0.1841.
Here, we have,
It should be noted that from the information illustrated, Wechsler Adult Intelligence Scale scores are approximately Normal, with a mean of 100 and a standard deviation of 11.
The formula to use will be:
P(a < Z < b) = P(Z < b) – P(Z < a)
a = lower value
b = higher value
Z = z value
It should be noted that the proportion of adults with scores above 110 will be:
= P(x > 110)
= P(z > 110 - 100/11)
= P(z > 0.90)
= 1 - 0.8159
= 0.1841
Therefore, this illustrates those that has scores of more than 110.
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Osing Trig to Find a Side Apr 06, 5:40:44 PM In AOPQ, the measure of ZQ=90°, the measure of Z0=26°, and QO = 4.9 feet. Find the length of PQ to the nearest tenth of a foot. P (hypotenuse) X (opp. of 20) 2009 Q 4.9
Answer:5.4
Step-by-step explanation:
Arthur wrote that 15 – 14.7 = 3.
Use the drop-down menus to explain why 3 is incorrect.
the point is supposed to be in front of the three
.3
Answer:
the answer is 0.3
Step-by-step explanation:
I hoped this helped
A pool manager balances the pH level of a pool. The price of a bucket of chlorine tablets is $90, and the price of a pH test kit is $11. The manager uses a coupon that applies a 40% discount to the total cost of the two items. How much money does the pool manager pay for each item?
Answer:
The chlorine tablets are $36 and the pH test kit is $4.40.
Step-by-step explanation:
So what I first did was add 90+11 (because $90 for the chlorine tablets and $11 for the pH kit). The answer you should get is 101. From their I did 101 multiplied by 40% or 101 multiplied by .40 (40% and 0.40 are the same thing). You now get $40.4.
Now I did 90·40%. I got $36
Then I did 11·40%. I got 4.4
I added them up and got $40.4 which was my new price so now we know that the chlorine tablets are $36 and the pH test kit is $4.40.
PLEASE HELP!! I DON'T UNDERSTAND!!!!! I WILL MARK!!!!
Answer:
2
Step-by-step explanation:
first use order of operations.
1/2(4^2)-6
1/2*16-6
then simplify to get:
8-6=2
Answer: 2
Step-by-step explanation:
The question is asking you to substitute the b with 4 and find the solution to the expression.
[tex]\frac{1}{2}b^{2} -6[/tex]
[tex]=\frac{1}{2}(4)^{2} -6[/tex]
[tex]=\frac{1}{2}(16) -6[/tex] (PEMDAS so you do the exponent first)
[tex]=8 -6[/tex] (PEMDAS so you do the multiplication first)
[tex]=2[/tex]
Hang was trying to factor 10x^2 + 5x she found that the greatest common factor of these terms was 5x and made an area model what is the width of the area model
Width of Heng's area model is 2x + 1
Step-by-step explanation:
Given:
Greatest common factor is 5x
To Find:
The width = ?
Solution:
let the be the area
And 5x be the length
Then area = length x width
Now rewriting the formula for width, we get
Width =
Substituting the values in the above formula
Width =
Width = 2x + 1
Pls help, answer righhand I’ll mark brainly and you big smart!
Answer:
A. and C.
Step-by-step explanation:
Just remember that to find the roots, use the equation:
(-b +/- sqrt[b^2 - 4ac])/2a
I would appreciate Brainliest, but no worries.
The integrat (cos(x - 3) dx is transformed into L' (t)dt by applying an appropriate change of variable, then g(t) i g(t) = 1/2 cos (t-3/2) This option g(t) = 1/2 sin(t-3/2)
The integrat (cos(x - 3) dx is transformed into L' (t)dt an g(t) = 1/2 sin(t-3/2) is incorrect. The correct option g(t) = 1/2 cos(t-3/2).
To transform the integral ∫cos(x - 3)dx into L'(t)dt using an appropriate change of variable, the substitution method make the substitution:
t = x - 3
To find dt, differentiate both sides of the equation with respect to x:
dt = dx
substitute these expressions into the integral:
∫cos(x - 3)dx = ∫cos(t)dt
The integral has been transformed into ∫cos(t)dt.
regarding the options for g(t),
Option 1: g(t) = 1/2 cos(t-3/2)
Taking the derivative of g(t) with respect to t,
g'(t) = -(1/2)sin(t - 3/2)
Option 2: g(t) = 1/2 sin(t-3/2)
Taking the derivative of g(t) with respect to t,
g'(t) = (1/2)cos(t - 3/2)
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Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.)
f(x) = 3x2/3 − 2x
I keep getting stuck at taking the first derivative and solving for critical points. So please show all work and even some of the tedious algebra bits included so I can see where I'm messing up?
The function f(x) = 3x²/3 - 2x has no intercepts, a relative minimum at (1, -1), no points of inflection, and no asymptotes.
Intercepts: To find the x-intercepts, we set f(x) equal to zero and solve for x:
0 = 3x²/3 - 2x
0 = x² - 2x
0 = x(x - 2)
x = 0 or x = 2
Therefore, both x = 0 and x = 2 are not actual x-intercepts, but rather double roots.
Relative Extrema: To find the relative extrema, we take the derivative of f(x) and set it equal to zero,
f'(x) = 2x - 2
0 = 2x - 2
2 = 2x
x = 1
Substituting x = 1 back into the original function, we find f(1) = -1. Therefore, the relative minimum occurs at (1, -1).
f''(x) = 2
Since the second derivative is a constant, it never equals zero. Therefore, there are no points of inflection for this function.
Asymptotes: To determine if there are any asymptotes, we examine the behavior of the function as x approaches positive or negative infinity. Since the highest power of x in the function is 2, the graph does not approach any vertical asymptotes.
For horizontal asymptotes, we look at the limits as x approaches positive or negative infinity:
lim(x→∞) f(x) = lim(x→∞) (3x²/3 - 2x) = ∞
The limits approach positive infinity in both cases, indicating that there are no horizontal asymptotes. Graphically, the function represents a parabola that opens upwards, with a relative minimum at (1, -1).
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Roy received math test scores of 05, 90, 90, and 85.
7. What is Roy's median test score?
8. What score would Roy need to get on
his next test to have a mean of 92
Median = 87.5 Sorry about the other one
Which equation represents a line which is perpendicular to the line
7x + 3y = -18?
Answer:
c y=6x+4
Step-by-step explanation:
Sami cut 6 and three fourth inches off a long roll of paper if the row 36 and one third inches long how long was the original roll of papers
Answer:
43 1 ÷12
Step-by-step explanation:
The computation of the length of the original roll of papers is shown below:
36 1 ÷3 and 6 3 ÷ 4 together
Now convert the above fractions into a number
36 1 ÷ 3 = 109 ÷3
And,
6 3 ÷4 = 27 ÷ 4
Now add these two numbers i.e.
109 ÷3 + 27 ÷ 4
= 436 + 81 ÷ 12
= 517 ÷12
= 43 1 ÷12
someone help please!! oh and pls don’t put any links
Answer:
10 visits
Step-by-step explanation:
So first let's make an equation, 7.74x + 8.93= 86.33. When you solve for x you get 10.
6(x-2)=-18 what does x=
Answer:
x = -1
Step by step explanation:
Distribute 6
6x-12= -18
Add 12 to both sides
6x= -6
Divide both sides by 6
x= -1
Hope this helps
Find the value of x for which / || m
Answer:
Step-by-step explanation:
Show the enteiws to close $2000 in expense, $5000 in revenue, and
$500 in dividens.
To close the $2,000 in expenses, $5,000 in revenue, and $500 in dividends, we need to transfer these amounts to the appropriate accounts and close the temporary accounts at the end of the accounting period. Here are the journal entries to close these amounts:
Close Expenses:
Date | Account | Debit | Credit
End of Year | Expenses | $2,000 |
| Income Summary | | $2,000
Close Revenue:
Date | Account | Debit | Credit
End of Year | Income Summary | $5,000 |
| Revenue | | $5,000
Close Dividends:
Date | Account | Debit | Credit
End of Year | Retained Earnings | $500 |
| Dividends | | $500
After these closing entries, the balances of the temporary accounts (Expenses, Revenue, and Dividends) will be zero, and their respective amounts will be transferred to the Income Summary and Retained Earnings accounts. The Income Summary account will show the net income (revenue minus expenses) for the period.
Please note that the specific account titles may vary depending on the company's chart of accounts, so make sure to use the appropriate account titles according to your specific chart of accounts.
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