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Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is a...
Stochastic models. DO NOT COPY ANSWER FROM SOMEWHERE ELSE, ONLY ANSWER IF YOU KNOW THE ANSWER. Th...
Stochastic models. DO NOT COPY ANSWER FROM SOMEWHERE
ELSE, ONLY ANSWER IF YOU KNOW THE ANSWER. Thank you.
(1) The pdf namely, fx(x) of a RV, x is distributed as follows: In the range (0x <1) Otherwise ft(x)--x (i) Find the pdf of: y 8x3 in the monotonically increasing in the given range ofxii determine the range ofy; and, (iii) decide the mean of y Answer hint: pdf(y) Ly136) (2) The pdf namely, fx(x) of a RV, x is distributed...
Show all work Question # A.1 (a) Given the CDF of a RV. x is specified...
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Question # A.1 (a) Given the CDF of a RV. x is specified as follows: Fx(x) = = = 0 B x (x/3) 1 in the range (x<0) in the range (0<x<+1) in the range (x > 1) Determine the following: (i) Value of B: (i) pdf of x: (111) pdf of y under the transformation y = (ax + b) where a and b are constants; (iv) range of the transformed RV, y and sketch the...
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the rand...
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3)
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise...
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
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)
The PDF of random variable X and the conditionalPDF of random variable Y given X are...
The PDF of random variable X and the conditionalPDF of random variable Y given X are fX(x) = 3x2 0≤ x ≤1, 0 otherwise, fY|X(y|x) = 2y/x2 0≤ y ≤ x,0 < x ≤ 1, 0 otherwise. (1) What is the probability model for X and Y? Find fX,Y (x, y). (2) If X = 1/2, nd the conditional PDF fY|X(y|1/2). (3) If Y = 1/2, what is the conditional PDF fX|Y (x|1/2)? (4) If Y = 1/2, what is...
Question Let X be a continuous random variable with the following probability density function (pdf) 0.5e...
Question Let X be a continuous random variable with the following probability density function (pdf) 0.5e fx (x) = { 0.5e-1 x < 0. <>0.. (a) Show that fx (x) is a valid pdf. (b) Find the cumulative distribution function Fx (.x). (e) Find F='(X). (d) Write an algorithm to generate a sample of size 1000 from the distribution of X using the inverse-transform method. Be as precise as possible.
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)
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = -...
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = - 0<r<1 (1) 0 :otherwise, Xa, n>2, be iid. random variables with pdf where 0> 0. Let X. X2.... given by (1) (a) Let Ylog X, where X has pdf given by (1). Show that the pdf of Y is Be- otherwise, (b) Show that the log-likelihood given the X, is = n log0+ (0- 1)log X (0 X) Hence show that the maximum likelihood...
Suppose X is an exponential random variable with PDF, fx(x) exp(-x)u(x). Find a transformation, Y g(X) so tha...
Suppose X is an exponential random variable with PDF, fx(x) exp(-x)u(x). Find a transformation, Y g(X) so that the new random variable Y has a Cauchy PDF given 1/π . Hint: Use the results of Exercise 4.44. ) Suppose a random variable has some PDF given by ). Find a function g(x) such that Y g(x) is a uniform random variable over the interval (0, 1). Next, suppose that X is a uniform random variable. Find a function g(x) such...
Stochastic models. DO NOT COPY ANSWER FROM SOMEWHERE
ELSE, ONLY ANSWER IF YOU KNOW THE ANSWER. Thank you.
(1) The pdf namely, fx(x) of a RV, x is distributed as follows: In the range (0x <1) Otherwise ft(x)--x (i) Find the pdf of: y 8x3 in the monotonically increasing in the given range ofxii determine the range ofy; and, (iii) decide the mean of y Answer hint: pdf(y) Ly136) (2) The pdf namely, fx(x) of a RV, x is distributed...
Show all work
Question # A.1 (a) Given the CDF of a RV. x is specified as follows: Fx(x) = = = 0 B x (x/3) 1 in the range (x<0) in the range (0<x<+1) in the range (x > 1) Determine the following: (i) Value of B: (i) pdf of x: (111) pdf of y under the transformation y = (ax + b) where a and b are constants; (iv) range of the transformed RV, y and sketch the...
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3)
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
Question Let X be a continuous random variable with the following probability density function (pdf) 0.5e fx (x) = { 0.5e-1 x < 0. <>0.. (a) Show that fx (x) is a valid pdf. (b) Find the cumulative distribution function Fx (.x). (e) Find F='(X). (d) Write an algorithm to generate a sample of size 1000 from the distribution of X using the inverse-transform method. Be as precise as possible.
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)
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = - 0<r<1 (1) 0 :otherwise, Xa, n>2, be iid. random variables with pdf where 0> 0. Let X. X2.... given by (1) (a) Let Ylog X, where X has pdf given by (1). Show that the pdf of Y is Be- otherwise, (b) Show that the log-likelihood given the X, is = n log0+ (0- 1)log X (0 X) Hence show that the maximum likelihood...
Suppose X is an exponential random variable with PDF, fx(x) exp(-x)u(x). Find a transformation, Y g(X) so that the new random variable Y has a Cauchy PDF given 1/π . Hint: Use the results of Exercise 4.44. ) Suppose a random variable has some PDF given by ). Find a function g(x) such that Y g(x) is a uniform random variable over the interval (0, 1). Next, suppose that X is a uniform random variable. Find a function g(x) such...
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