Let Y be a continuous random variable with cumulative distribution function: B A C C D D E √2 In √√2 In ¹ (C) (D) a-2√In2 (E) a +2√In2 -{i- a + F(y) = where a is a constant. What is the 75th percentile of Y? (A) F(0.75) (B) a- 1-e-(y-a)², for y sa otherwise

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Q: For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))

A: Given, Two random variables X and Y such that X~Exp(0.5) and Y|X=x ~N(5,x2)

Q: let x has the p.d.f f(x) = {3xe* 3xe-V3x 0 < x < c0 0.W By m.g.f find the mean and variance of the…

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Q: Let rt be a log return. Suppose that r0, r1, . . . are i.i.d. N(0, 0.01^2). (a) What is the…

A: we have given - rt be a log return. Suppose that r0, r1 . . . are i.i.d. N(0, 0.0001). a) since ,…

Q: Let X be a random variable with E(X)= 1 and E[X(X-1)]=4,then evaluate Var(2-3X).

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A: Here,fx=dfxdx=dcx-14dx=4cx-13                                    ;1&lt;x≤3   Now, find c using the…

Q: Suppose that E and F are two events such that Pr[E] = 17/29, Pr[F] = 13/29, and Pr[EN F] = 8/29.…

A: Given, P(E) = 1729P(F) = 1329P(E∩F)=829

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A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Let X and Y be random variables with Var(X)=0.64, Var(Y)=0.81, and Cov(X,Y) = 0.5. Find each of the…

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Q: Let Y be a continuous random variable with f(y) = {1123 0, Find the mean (µ) and variance (0²) of Y.…

A: Method: integration of continuous distribution.The pdf of continuous random variable  is:

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A: From the provided information, Mean (λ) = 2 X~exp(2)

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Q: C1. Let X be a continuous random variable with PDF f(æ) = (2 – æ) for -1 1)? (c) Calculate the…

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