Let X1 d= R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y := X1 + X2 and U := X1X2.
(a) Find the state space of Y and derive the cdf FY and pdf fY
of Y .
(You may wish to use {X2 = i}, i = 0,1, as a partition and apply
the total probability formula.)
(b) Compute the mean and variance of Y in two different ways, one is through the pdf of Y and the other is using the sum of two independent random variables.
(c) Calculate E(U) and V(U).
(d) Find the state space of U and calculate the cdf FU of U.
(e) Calculate Cov(U, X2) and ρ(U, X2).
Let X1 d= R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y :=...
Let X1 d = R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y := X1 + X2 and U := X1X2. (a) Find the state space of Y and derive the cdf FY and pdf fY of Y . (You may wish to use {X2 = i}, i = 0,1, as a partition and apply the total probability formula.) (b) Compute the mean and variance of Y in two different ways, one is through the pdf of...
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Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof using the de finition of distribution function that the the distribution function of Z =Y Xit(1-Y)X2 is F = pF14(1-p)F2 Don't use generatinq moment functions, characteristic functions) Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter...