Let X be a discrete random variable with moment generating function 1 M(t) 6. (e²t + e=) (e²r + e³r + et"). Find the variance of X. 96 2.9167 15.1667 88 3.456

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A: Moment generating function:

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A: The moment generating function of x is given by: Mxs=EesX=13es+23e2s+0e3sMxs=13es+23e2s

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A: Given x1, x2, . . ., xn be random sample from the exponential distribution with parameter λ.

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A: X~Pois(λ) P(X=x)=e-λ λx/x! x=0,1,2,3,..,..

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Q: b) Consider a random variable K with parameter p, whose probability mass function (PMF) is given by…

A: Since you have posted more than one question we will solve first question for you according to our…

Q: Consider a random variable K with parameter p, whose probability mass function (PMF) is given by…

A: Solution: From the given information, the probability mass function is

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Q: 21. Let the random variable X have the moment generating function e3t M (t) -1 <t < 1. 1- t2 ' What…

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A: We want to find the expected value E(Z)=X1+X2+X3+X4

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Q: Let X be a random variable whose moment generation function is 1 given by Mx(t) - (10+ 2e)2, teR.…

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Q: Suppose X1, X2, X3 are m generating functions, Mx, (t) = e²²², Mx, (t) = e²t + 3t², and Mx, (t) = (²…

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A: Given information: The probability density function of the random variable X is as given below:

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Q: 3. Find a PDF of a random variable X whose CDF is given by Fx(x) = (1-e*)[0,00) (x).

A: Solution

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Q: tion MX(t) = e 3t+8t2 , find the moment g

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Q: 11. Suppose X and Y are independent continuous random variables uniformly dis- tributed on the…

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A: The given pdf is shown below:

Q: (a) Let Y be a random variable distributed as X. Determine E(VY) in terms of r.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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Q: Let X be a Poisson random variable with parameter 1> 0. (a) Calculate EX, EX(X – 1) and EX(X – 1)(X…

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Q: Let Y be a discrete random variable.  Let c be a constant.   PROVE  Var (Y) = E (Y2) - E (Y)2

A: We have to deduce the formula of variance.

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Q: A Irwin-Hall distributed random variable with parameter n is a random variable X such at X = U1 + U2…

A: From the given information, a Irwin-Hall distributed random variable with parameter n is a random…