Let random variable Y follows Bi(200, .3), Find P(Y 63), P(59 Y 64).
Let Y be a random variable with p(y) given in the accompanying table. Find E(Y), E(1/Y), E(Y2-1), and V(Y). y 1 2 3 4 p(y) .4 .3 .2 .1
Let Y be a binomial random variable with parameter p. Find the sample size necessary to estimate p to within .05 with probability .95 if p is thought to be approximately .9.
4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let ?? = √?? 3 3 . Find the probability distribution of V 3 4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let V 3 Find the probability distribution of.
2040DE_Quiz3_DiscreteRV Let X be a discrete random variable that follows a geometric distribution with p = 0.44. What is P(X < 3)? Round your answer to at least 3 decimal places. Number
(2) Let Y be a binomial random variable with parameters n and p. Remember that E(Y) V(Y)p1 -p) We know that Y/n is an unbiased estimator of p. Now we want to estimate the variance of Y with n(2(1 (a) Find the expected value of this estimator (b) Find an unbiased estimator that is a simple modification of the proposed estimator
Let the random variable X have a uniform distribution on [0,1] and the random variable Y (independent of X) have a uniform distribution on [0,2]. Find P[XY<1].
Problem 1. Let x be a random variable which approximately follows a normal distribution with mean i = 1000 and o = 200. Use the z-table (attached to this test), calculator, or computer software to find the following: Part A. Find P(> 1500). Part B. Find P(x < 900). Part C. Find P(900<x<1500).
Let X be a discrete random variable with 1 P(X = 1) = P(X = 2) = P(X = 3) = P(X= 4) = Then given X = x, we roll a fair 4-sided die 3 times. (The 4-sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y|X]. Hint: Remember E[Y | X] is a random variable, so X will be part...
3. [30 pts.] Let X be a Gaussian random variable N (0,0). Find the PDF, fy(y), of the random variable: Y = X3
Let the random variables x and y have joint pdf as follows: 4 x < 1,0< y< 3 0 3 2) (round off to third decimal place). Find P(X>