A random variable Y has a density fx(x) (a) What is the third quartile of X?...
4.4.19 Random variableX has PDE fx(a)-1/4 -1s-33, 0 otherwise Define the random variable Y by Y = h(X)X2. (a) Find E[X and VarX (b) Find h(E[X]) and Eh(X) (c) Find ElY and Var[Y .4.6 The cumulative distribution func- tion of random variable V is 0 Fv(v)v5)/144-5<7, v> 7. (a) What are EV) and Var(V)? (b) What is EIV? 4.5.4 Y is an exponential random variable with variance Var(Y) 25. (a) What is the PDF of Y? (b) What is EY...
Problem 5. The joint density of X and Y is given by e" (z+y) fx.-otherwise. İf 0 < x < oo, 0 < y < 00, Consider the random variable Z-; a) Find the cumulative distribution function of Z b) What is the probability density function of Z?
PLEASE SOLVE FULLY WITH NEAT HANDWRITING AND EXPRESS FINAL ANSWER WITH BOXES!! Suppose that the density (pdf) function for a random variable X is given by fx)or 0s x s2 and fx) 0 otherwise. What is Suppose that the density (pdf) function for a random variable X is given by f(x)--for 0 SX 2 and f(x)-0 otherwise, what is the probability P(0.5 1)? Round your answer to four decimal places. X Suppose that the density (pdf) function for a random...
Let X be a random variable with density function fX (x)= cx(1−x), if0<x<1, 0 ,otherwise. (a) What is the value of c? (b) What is the cumulative distribution function FX for X? (c) What is the probability that X < 1/4?
3,40 A random variable X has probability density function fx(x) = 1 0<x< 1. Find the probability density function of Y = 4x3 - 2.
6. A random variable Y has density function fy(a)Ky(where y 2 2 (and zero otherwise) and b > 0. This random variable is obtained as the transformation Y-g(X) of the random variable X with density function fx(x) e, a 2 0. Function g(x) is an increasing function in r (a) Show that Kb2b. (b) Determine the transformation g(. in terms of b. Hint: For part (b), carefully read Wackerly 6.4 on how the method of transformations is derived. On p.311,...
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...
Suppose density function positively valued continuous random variable X has the probability a fx(x)kexp 20 fixed 0> 0 for 0 o0, some k > 0 and for (a) Find k such that f(x) satisfies the conditions for a probability density function (4 marks) (b) Derive expressions for E[X] and Var[X (c) Express the cumulative distribution function Fx(r) in terms of P(), the stan dard Normal cumulative distribution function (8 marks) (8 marks) (al) Derive the probability density function of Y...
[1] The joint probability density function of two continuous random variables X and Y is fx,x(x, y) = {6. sc, 0 <y s 2.y = x < 4-y otherwise Find the value of c and the correlation of X and Y.
2.9.10 Suppose X has density fX(x) = x3/4 for 0 < x < 2, otherwise fx(x) = 0, and Y has density fr (y)-5y4/32 for 0 < y < 2, otherwise fr (y)-0. Assume X and Y are independent, and let Z = X + Y (a) Compute the joint density fx.r(x. y) for all x, y e R (b) Compute the density fz(z) for 2.