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Q1) A-Random variable X has the following Probability Density Function (PDF) fr(x)= 부.lel s 3. (0,...
X is a positive continuous random variable with density fX(x). Y = ln(X). Find the cumulative...
X is a positive continuous random variable with density fX(x). Y
= ln(X).
Find the cumulative distribution function (cdf) Fy(y) of Y in terms of the cdf of X. Find the probability density function (pdf) fy(y) of Y in terms of the pdf of X. For the remaining problem (problem 3 (3),(4) and (5)), suppose X is a uniform random the interval (0,5). Compute the cdf and pdf of X. Compute the expectation and variance of X. What is Fy(y)?...
P7 continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The...
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
For a continuous random variable X with the following probability density function (PDF): fX(x) = (...
For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)
is a continuous random variable with the probability density function (x) = { 4x 0 <=...
is
a continuous random variable with the probability density
function
(x) = {
4x 0 <= x <= 1/2
{ -4x + 4 1/2 <= x <= 1
What is the equation for the corresponding cumulative density
function (cdf) C(x)?
[Hint: Recall that CDF is defined as C(x) = P(X<=x).]
We were unable to transcribe this imageWe were unable to transcribe this imageProblem 2. (1 point) X is a continuous random variable with the probability density function -4x+41/2sxs1 What is...
2) A random variable X has the density function: fr(x) =[u(x-1)-u(x-3)]. Define event B (Xs 2.5)...
2) A random variable X has the density function: fr(x) =[u(x-1)-u(x-3)]. Define event B (Xs 2.5) (a) Find the cumulative distribution function, Fy (x). (b) Find the conditional distribution Fx (x|B). the mean E[X], and variance of X Fx(xB)= E[X)= Variance (e) Sketch both Fy(x) and Fx (x|B) on the same plot. Show all important values. (d) Let the output of random variable X above be applied to a square-law device according to Y 5X2. Find the mean value of...
I . (20%) Random variable X has the probability density function as ; Random variable Y...
I . (20%) Random variable X has the probability density function as ; Random variable Y 2X+1 0 otherwise a) Determine A b) Determine the Probability Distribution Function F, (x) c) Determine E(X) and ơx d) Determine the probability density function fy(y) and E(Y)
Between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
Between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero...
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
X is a positive continuous random variable with density fX(x). Y
= ln(X).
Find the cumulative distribution function (cdf) Fy(y) of Y in terms of the cdf of X. Find the probability density function (pdf) fy(y) of Y in terms of the pdf of X. For the remaining problem (problem 3 (3),(4) and (5)), suppose X is a uniform random the interval (0,5). Compute the cdf and pdf of X. Compute the expectation and variance of X. What is Fy(y)?...
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
is
a continuous random variable with the probability density
function
(x) = {
4x 0 <= x <= 1/2
{ -4x + 4 1/2 <= x <= 1
What is the equation for the corresponding cumulative density
function (cdf) C(x)?
[Hint: Recall that CDF is defined as C(x) = P(X<=x).]
We were unable to transcribe this imageWe were unable to transcribe this imageProblem 2. (1 point) X is a continuous random variable with the probability density function -4x+41/2sxs1 What is...
2) A random variable X has the density function: fr(x) =[u(x-1)-u(x-3)]. Define event B (Xs 2.5) (a) Find the cumulative distribution function, Fy (x). (b) Find the conditional distribution Fx (x|B). the mean E[X], and variance of X Fx(xB)= E[X)= Variance (e) Sketch both Fy(x) and Fx (x|B) on the same plot. Show all important values. (d) Let the output of random variable X above be applied to a square-law device according to Y 5X2. Find the mean value of...
I . (20%) Random variable X has the probability density function as ; Random variable Y 2X+1 0 otherwise a) Determine A b) Determine the Probability Distribution Function F, (x) c) Determine E(X) and ơx d) Determine the probability density function fy(y) and E(Y)
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
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