g(x?)dx for "all" functions g: R R . Suppose that a random variable X satisfies E...
Exercise 3.37. Suppose random variable X has a cumulative distribution function F(x) = 1+r) 720 x < 0. (a) Find the probability density function of X. (b) Calculate P{2 < X <3}. (c) Calculate E[(1 + x){e-2X].
The random variable X has the probability density function (x)a +br20 otherwise If E(X) 0.6, find (a) P(X <름) (b) Var(x)
Problem 9: Suppose X is a continuous random variable, uniformly distributed between 2 and 14. a. Find P(X <5) b. Find P(3<X<10) c. Find P(X 2 9)
Suppose the density for a random variable is given by the following: f(x) = Cz" for 1 < x < 2, and f(x) = 0 otherwise. Find the value of C, and then find the mean of this random variable.
Let X be an exponential random variable such that P(X<26) = P(X > 26). Calculate E[X|X > 28]. Answer: CHECK
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. 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).
4B-03] Suppose that we are given the random variable X with pdf f(x) = 1-x/2 for 0<x<2, and 0 otherwise. Obtain P(X1). (Round to 2 decimals) Your Answer: Answer
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
Suppose X is a continuous random variable having pdf (1+x, -1 < x < 0, f(x) = { 1 – x, 0 < x <1, lo, otherwise (a) Find E(X2). (b) Find Var(X2).