Let X have the probability distribution f(x) = 2(x+1)/ 9 , −1 < x < 2, 0, elsewhere. Find the probability distribution of the random variable Y = X2 .
Let X have the probability distribution f(x) = 2(x+1)/ 9 , −1 < x < 2,...
Let X be a binomial random variable with the probability distribution f(x) shown below. Find the probability distribution of the random variable Y = x2. 3-X ; x = 0, 1, 2, 3 f(x) = elsewhere Complete the probability distribution g(y) of the random variable Y = x². 3-2/ , y=0,1 g(y) = elsewhere (Type exact answers, using radicals as needed. Use integers or fractions for any numbers in the expressions. Simplify your answers. Use a comma to separate answers...
- ACUJU 1. (6%) Let X be a random variable with probability distribution (1+x **,-1<x< 1 0, elsewhere Find the probability distribution of the random variable Y = X2.
Let X have probability density function f(2)= k(1+x) -3 for 0 < x < oo and f(x) = 0 elsewhere. a. Find the constant k and Find the c.d.f. of X. b. Find the expected value and the variance of X. Are both well defined? c. Suppose you are required to generate a random variable X with the probability density function f(x). You have available to you a computer program that will generate a random variable U having a U[0,...
Let X be a binomial random variable with the probability distribution f(x) shown below. Find the probability distribution of the random variable Y =X4. 3-x f(x)= H , = 0, 1, 2, 3 f(x) = { elsewhere Complete the probability distribution g(y) of the random variable Y = X*. elsewhere (Type exact answers, using radicals as needed. Use integers or fractions for any numbers in the expressions. Simplify your answers. Use a comma to separate answers as needed.) icals as...
WILL THUMBS UP IF DONE NEATLY AND CORRECTLY! Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...
1. Let X be a continuous random variable with the probability density function fx(x) = 0 35x57, zero elsewhere. Let Y be a Uniform (3, 7) random variable. Suppose that X and Y are independent. Find the probability distribution of W = X+Y.
2.a. Let X1, X2, ..., X., be a random sample from a distribution with p.d.f. (39) f( 0) = (1 - 1) if 0 < x <1 elsewhere ( 1 2.) = where 8 > 0. Find a sufficient statistic for 0. Justify your answer! Hint: (2(1-)). b. Let X1, X2,..., X, be a random sample from a distribution with p.d.f. (1:0) = 22/ if 0 < I< elsewhere where 8 >0. Find a sufficient statistic for 8. Justify your...
P7 continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
Let the conditional probability distribution of Y given π be elsewhere In this problem we will assume that π is a random variable and that the marginal distribution of π has a probability density function given by: f(n) = 0 elsewhere (a) Find the joint probability density function of Y and π, that is f(y, π). Please find the marginal probability distribution of Y, ). (c) Find the conditional distribution of f( y). (d) What is the mean and variance...
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer. a. Find the constant k. b. Find the expected value M(S) = E(esX) as a function of the real numbers s. Compare the values of the derivative of this function M'(0) at 0 and the expected value of a random variable having the probability function above. c. What distribution has probability function f(x)? Let X1, X2 be independent random variables both...