(a) Let Z = vX. Show that the density function of Z is given by %3| (-). fz(z) = 2a exp z > 0.

Q: a. What value of c will make f(x) a valid density? b. What is P(X = 1)? What about P(X = 1 or X =…

A: The value of c that makes probability density function valid is obtained below: From the given…

Q: Suppose f(x)=3x2, 0<x<1 is a density function of X.  Find P(1/2<X<2).

A: We have given that,  Let x is a random variable having probability density function is,  f(x) =…

Q: The value of c

A: The given density function is, fx=cx2      if 0&lt;x&lt;30          otherwise It is known that the…

Q: (a) Find k. (b) Find cdf F(X).

A: Here we have given the pdf of continuous Random variable X We have to find the value of K and…

Q: Find a constant b > 0 so that the function e3x fx (*) = 0 < X <b 4 elsewhere is yalid density…

A:

Q: A random variable Y has the density function { Se', y<0 otherwise f(y) = Find E(Y ³).

A:

Q: (a) Show that f(x) = 3x2 for 0 &lt; x &lt; 1 represents a density function.(b) Sketch a graph of…

A: Any function is a probability density function if it satisfy following two condition  Now, lets…

Q: (d) What is the median checkout duration ? [solve 0.5 = F()]. (e) Obtain the density function f(x).…

A: Since you have asked multiple questions, we will solve first three subparts for you. To get…

Q: Verify that the integral of the beta density from −qto q equals 1 for(a) α = 2 and β = 4;(b) α = 3…

A: The Beta density function is given by: We need to prove:

Q: A continuous random variable X that can assume values between x = 3 and x = 6 has a density function…

A: A continuous random variable X that can assume values between  has a density function given byFor…

Q: Find E(X)

A:

Q: Suppose you choose a real number X from the interval [2, 10] with a density function f(

A: Given that the density function for X is, fx=148x, 2≤x≤10

Q: Problem 8: Consider the density function f(x) = a) Evaluate k. b) Find F(x). c) Use F(x) to evaluate…

A: Given: f(x)=kx4,x&gt;10,x≤1

Q: If X and Y are jointly continuous with joint density function fx,y(z,y), show that X + Y is…

A: Let X and Y are jointly continuous with joint density function fX,Y(x,y) We have to prove that X+Y…

Q: The random variables X and Y have joint density function f(x, y) 2 (x + 2y), 0 < z < 1, 0< y<1. Find…

A: The joint density function of (x,y) is, The marginal density of X is,           Hence, the…

Q: 8. Show that the gamma density function f(x, λ, r) integrates to 1

A:

Q: 1. Find the density of Y = 1- e-ax when X ~ Exp(X). Note that the density of X is if r > 0, ,…

A: