1. Assume X is Binomial (n, p), where the constant p (0,1) and the integer n...
2. Assume X is a random variable following from N(μ, σ2), where σ > 0. (a) Write down the pdf of X (b) Compute E(X2). (b) Define YFind the distribution of Y.
For n = 40 and 1 = 0.4, use the normal distribution to approximate the following probabilities. a. X=25 b. X> 25 c. X s 25 d. X<25 . a. The approximate probability that X = 25 is (Round to four decimal places as needed.)
Suppose that X ~ unif(0,1). Find the distribution of Y = (1 – X)-B – 1 for some fixed B> 0. (Name it!)
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
Question 5: Consider the following choice (where pe 0,1), (0,1), and p+q<1): x=($40.p: $10,4; $0,1-p-9) vs. y= (a) For what values of p and does lottery x dominate lottery y? (b) For what values of p and q does lottery y dominate lottery x?
is independent of X, and e Problem 3 Suppose X N(0, 1 -2) -1 <p< 1. (1) Explain that the conditional distribution [Y|X = x] ~N(px, 1 - p2) (2) Calculate the joint density f(x, y) (3) Calculate E(Y) and Var(Y) (4) Calculate Cov(X, Y) N(0, 1), and Y = pX + €, where
3. Suppose X ~ Beta(a, β) with the constants α, β > 0, Define Y- 1-X. Find the pdf of Y
1. The probability mass function of a random variable X is given by Px(n) bv P Yn (a) Find c (Hint: use the relationship that Σο=0 (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3) n-0 n! ex)
3) Suppose X~N(0,1) and Y~N(2,4), they are independent, then is incorrect. 6 X-Y N(-2,5) D Var(X) < Var(Y) SupposeX-N(Aof) and Y-N(H2,σ ), they arc indcpcndcnt, thcn in the following statementss incorrect 4) 5) Suppose X~NCHiof) and Y~NCHz,σ ), they are independent, if PCIX-Hik 1) > PCIY _ μ2I 1), then ( ) is correct.
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)