Suppose that X has CDF Exercise 24.22. Suppose that X has CDF 0 If x <...
The random variable X has CDF 0 x<-1, 0.2 -1s<O, 0.7 OS<1, 1 21. Fx () (a) Draw a graph of the CDF. (b) Write Px(x), the PMF of X. Be sure to write the value of all a from -oo to oo.
2. A random variable X has a cdf given by F(x) = 1 . x < 0 0 < x < 1 <3 x > 3 11, (f) What is P(X = 1)? (g) Find E(X), the expectation of X. (h) Find the 75th percentile of the distribution. Namely, find the value of 70.75 SO that P(X < 70.75) = F(710.75) = 0.75. (i) Find the conditional probability P(X > X|X > 3).
Problem # 10, Let X be a random variable with CDF: 0 (x + 5)2/144-5 < x < 7 Ex (x) = X(r Find E(X], , and E[X"].
Let X be a random variable with CDF z<0 G()=/2 0 <IS2 z>2 1 Suppose Y = X2 is another random variable, find (a) P(1/2 X 3/2), (b) P(1s X< 2) (c) P(Y X) (d) P(X 2Y). (f) If Z VX, find the CDF of Z. (d) P(X+Y 3/4)
2) Suppose that X has density function f(a)- 0, elsewhere Find P(X < .3|X .7).
The random variable X has CDF 0 <-1, Ex(x) = 0.2 -1 < 0, 0.7 0 x<1, 1 21. (a) Draw a graph of the CDF (b) Write Px(), the PMF of X. Be sure to write the value of Px(a) for all r from-oo to oo. Given the random variable X in problem ii), let V g X)X. (a) Find P(v). (b) Find Fy(v). (c) Find EIV]
Question 13 The cumulative distribution function of X is given by Fx (x) = {-kr <0 0<x<2 > 2 Find (a) the value of k, (b) the probability density function fx (x), (c) the median of X, (d) the variance of X.
< 0) = 1/3, and Exercise 9.8. Suppose X has an N(u,02) distribution, P(X P(X < 1) = 2/3. What are the values of u and o?!
3. (10 points) Let X be a continuous random variable with CDF for x < -1 Fx(x) = { } (x3 +1) for -1<x<1 for x > 1 and let Y = X5 a. (4 points) Find the CDF of Y. b. (3 points) Find the PDF of Y. c. (3 points) Find E[Y]
Suppose that the cdf of random variable X is Skex-3, X <4 11, X >4 Find k. (2 Points) Find the expected value of X. (2 Points)