Let X be a continuous random variable with density function be-bx for a > 0 otherwise , f(x) = where b> 0. - find M(t) the moment generating function of X, then what is E(x) ?

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A: Given information: The number X is chosen at random between 0 and 1.  fx=11-0,…

Q: fr(y) =(y-3)e Find the probability density of the sum W =X + Y.

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A: Check the solution in the explanation.Explanation:Check the image below for a detailed solution.

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Q: a) A continuous random variable Y has density function 3-2y f(y)={3 e „y > 0 ,elsewhere Find the…

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Q: Suppose that the random variables Y1 and Y2 have joint probability density function f(yn.2) given by…

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A: Given, The density function is, f(x)=kx2                              0≤x≤3

Q: technique to find the density function for the random variable Y. The density function should be…

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Q: (d) Are the random variables X and Y independent? Justify your answer.

A: To check independence of X and Y we have to find marginal pdfs of X and Y.

Q: (i) determine how to generate a random variate X. (ii) generate random variate X, uniformly…

A: For generating a random variate that follows a particular distribution, the inverse transform method…

Q: Question is attached.

A: (a)The value of c can be derived as follows:

Q: et it be the probability density function. [ f(x2= n-x 2(1-2). ax Let it be Y = e x=0,1,2, So E(Y)…

A: Solution

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Q: - Let Y and Y have the joint pdf f(x, y) = 6(1 - x-y), x+ y < 1, 0 < x, 0 < y, zero elsewhere…

A: The problem can be solved using the concept of marginal distribution and expectation. please find…

Q: Consider the following interesting probability mass function for a random variable X with A > 0 p(x)…

A: Probability Mass Function: A discrete function f(x) is said to be the probability mass function of…

Q: 9 Let the probability density of the two-dimensional random variable (5, n) be (4e", x>0; f(x)=10.…

A: The probability density function for the two variables are : fξ(x)=4e-4x ,x&gt;0fη(y)=6e-6y ,y&gt;0…

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Q: Sketch the graph of the probability density function over the indicated interval. F(x) = 1/20, [0,…

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Q: The probability density function of the gamma distribution is as follows. f (x) = Г(а) ßx , x>0, a,…

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Q: A random variable X has the density function f(x) = c/(x² + 1), where -<x < 0. (a) Find the value of…

A: a) The total probability is always 1. Using that we get:…

Q: A random variable 0~U(- ), find the probability density function of the random variable Y = tan 0

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Q: The density function of X is given by f(x) = a + bæ, 0< x < 1. (1) If E(X) = , find a and b. (2)…

A: density function of X is given by;f(x)=1+bx,  0≤x≤1

Q: Suppose that X, Y are jointly continuous with joint probability density function f( x, y){…

A: X and Y denote  jointly continuous rvs.The joint density function:

Q: (x + ax², 0 < x < 1 diğer fx (x) = 0,

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Q: One recognizes the integrand of Equation (23) as a r(a, 6) density, hence M (t) = (;)"(1) = (24) |3|…

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