Suppose X has pdf f(x)= {3/28x^2, x ∈ [−1, 3]
0 , otherwise
let Z = X^2. What is the pdf of Z?
Suppose X has pdf f(x)= {3/28x^2, x ∈ [−1, 3] 0 , otherwise let Z =...
19. A random variable X has the pdf f(x) = 2/3 0 otherwise if 1 < x 2 (a) Find the median of X. (b) Sketch the graph of the CDF and show the position of the median on the graph.
Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise Find CDF of X FInd pdf of Y
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
9. Let a random variable X follow the distribution with pdf f(z)=(0 otherwise (a) Find the moment generating function for X (b) Use the moment generating function to find E(X) and Var(X)
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...
3. Let X has the following pdf: {. -1 <1 fx(a) otherwise 1. Find the pdf of U X2. 2. Find the pdf of W X
D Question 3 10 pts The joint pdf of X, Y, and Z is given by f(x,y,z) = 8xyez for 0sxcys 1, z>0 (0 otherwise) What is the joint pdf of U=X/Y and V = Y? O g (u, u) = 8uu for 0 < u-u-1 (-0 otherunse) O g(u,) foru 1 0v1 (0 otherwise) O g (u, u) 4uv for 0 < u < 1; 0 < u < 1 ( 0 otherwise) O g (u, v) = 8uv2...
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise where c is a constant. a. Find the value of c. b. Find the mean of X. C. Find the variance of X. d. Find P(-1 < X < 2). e. Find P(X>1/2). f. Find the third quartile.
Let X and Y be continuous random variables with following joint pdf f(x, y): y 0<1 and 0<y< 1 0 otherwise f(x,y) = Using the distribution method, find the pdf of Z = XY.
Suppose X has the following Uniform distribution if 0<x<6 f(x)=\ & 0 otherwise a) Sketch the pdf of X b) What is Pr(X<4)? c) What is Pr(X<2|X<4)?