C1. Let X be a continuous random variable with PDF f(æ) = (2 – æ) for -1 < x < c and f(x) = 0 otherwise. (a) Calculate the CDF F of X, and hence find the constant c. (b) What is P(X > 1)? (c) Calculate the expectation and variance of X. (d) Let Y = (X² – 1). What is the expectation of Y?

Q: 5. (8 pts) X is a random variable with pdf Xe-xx>0 f(x) = { o/w and let Y = 1 - X/2. Find the pdf of…

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Q: Let u(X) be a nonnegative function of a random variable X. It can be shown that  P(u(X) >= c) = a)…

A: It is an important part of statistics. It is widely used.

Q: 1.4 Let X be a continuous random variable with pdf, fx(x), and fx (t+5) = fx (5 t) for all t> 0.…

A: Here, we have given a continuous random variables and also some condition is given. Then, we have to…

Q: (a) Find the expectation E (X) of X. E (X) = [] (b) Find the variance Var(X) of X. Varlx) = D

A: The following table shows the provided outputs of the discrete random variables, along with the…

Q: The values of x and their probabilities are listed below.  Calculate the intermediate products to…

A: x P(x) xP(x) 32 0.07 2.24 34 0.12 4.08 36 0.24 8.64 38 0.25 9.5 40 0.32 12.8 Total…

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

Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…

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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…

A: Part (a) Coefficient of correlation ρ(X,Y)The coefficient of correlation ρ  is defined…

Q: The values of x and their probabilities are listed below.  Calculate the intermediate products to…

A: Given that: x P(x) x * p(x) 32 0.07 2.24 34 0.12 4.08 36 0.24 8.64 38 0.25 9.50 40 0.35…

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A: It is given that  U=X1-X2, V=X1-X2. The inverse equation obtained is, X1=U+VV, X2=U-VV. a. The…

Q: Let X and Y have a bivariate normal distribution with mean vector (₁ = 3, μ2 = 1)', and standard…

A: The answer to the first sub question is 4.Please follow the below attachment for the solution.

Q: X and Y are independent and identically distributed random variables with ~ Exp(A). 2) Determine the…

A: Please see the next step for solution.

Q: Let X be a random variable with discrete pdf f(x) = x/8 if x = 1, 2, 5, and zero otherwise. Find:…

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Q: F(x,y) = { (x+y)/42 ; x = 1,2,3  y = 1,2                 0; elsewhere ] (i) Find the mean for the…

A: F(x,y) : { (x+y)/42 ; x=1,2,3 y=1,2  ; 0 elsewhere } Mean : E(X) = sum(x*P(x))

Q: Let X be a discrete random variable with pmf (a) Find the pmf for Y = X². (b) Find the pmf for U = X…

A: The PMF of random variable X is: f(x)=18      x=-214      x=-114      x=014      x=118       x=2  0…

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A: Solution

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Q: The density function of Xis (2(x-1), f(x)= (a) Find the mean E(4X+3); (b) Find the variance σ3x+2.…

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