4.144 Consider a random variable Y with density function given by f(y)=ke-²/2 a Find k. b Find the moment-generating function of Y. c Find E(Y) and V (Y). -∞

Q: a 3 P(X = x) = x = 0, 1, 2, 3 is a probability mass function. %3D %3D x2 +1' a Find the value of a.…

A: I am providing solution of question no. 3. Since, the function is a probability mass function, the…

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A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted

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A: Given

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A: Given that, the exponential random variable X with pdf f(x) = λe_λx,  x>0

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Q: Consider a random variable Y with density function given by f(y) = ke¯x³2 -00 < y < . a Find k. b…

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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Q: Q1-Let X and Y be two independent random variables with respective density functions: (32 f (x) =…

A: The density function of x is fx=32x3,                        x&gt;40…

Q: 1. Show that the density function f(x; a, B) has a relative maximum at x = a-1 a+B-2'

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Q: 2. [Transformations] Consider X ~ U(0, 1) with the probability mass function 1, x = (0,1) fx(x) = 0,…

A: Part (a):To find the support and probability density function (PDF) for Y=log(X), we need to first…

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A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: 3 The continuous random variable Y has a cumulative distribution function given by: y 2 where k is a…

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A: At first writing the p.d.f of  Chi-Square distribution and then proceed....

Q: 34.- Let X1,., Xn a random sample of the population with distribution Beta(a, 2), a > 0, ß = 2,…

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A: Question 5)The joint density function of and  is,