Suppose that X ~ unif(0,1). Find the distribution of Y = (1 – X)-B – 1...
1 x Suppose X has an exponential distribution, thus its pdf is given by fx (x) = 5e8,0 5x<0, 2> 0;0 0.w. a. Find E(X) b. Find E(X(X-1) c. Find Var (x)
1. Assume X is Binomial (n, p), where the constant p (0,1) and the integer n > 0. (a) Express PX > 0) in terms of n and p (b) Define Y = n-X. Specify the distribution of Y.
7. Suppose the random variable U has uniform distribution on [0,1]. Then a second random variable T is chosen to have uniform distribution on [O, U] Calculate P(T > 1/2)
-3x > 0 An exponential distribution is given by f(x) zero, x <0 Find the distribution of the random variable Y X2
Suppose X and Y are independent random variables with Exponential(2) distribution (Section 6.3). We say X ~ Exponential(2) if its pdf is f(x) = -1/2 for x > 0.
3. Suppose X ~ Beta(a, β) with the constants α, β > 0, Define Y- 1-X. Find the pdf of Y
(1 point) Find the solution of x²y" + 5xy' + (4 – 3x) y = 0, x > 0 of the form y=x" Wazek, k=0 where ao = 1. r = help (numbers) ak = , k=1,2,3,... help (formulas)
-. Show that if x ~ Unif(a, β) and μ-E(X) (so μ-(a + β)/2), then for integers r > 0, 0 r odd 12
9.) Suppose that X is a continuous random variable with density C(1- if [0,1] px(x) ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function. (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X
Let X have the pdf defined for 0<x<2. Let Y~Unif(0,1). Suppose X and Y are independent. Find the distribution of X-Y. fx() =