If X and Y are random variables, find E[YE(X|Y = y)]
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If X and Y are random variables, find E[YE(XY = y)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60abd4de-ba2d-4a53-b8fc-e1d2e0799cec%2Ffa96b83d-13f2-4e8f-88d2-3c6cceb97a4a%2F45vm0j_processed.jpeg&w=3840&q=75)
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by Bartleby Expert- Let X1, X2, . . . are independent indicator variables with different probabilities of success. That is, P(Xi = 1) = pi. Define Yn = X1 + X2 + . . . + Xn. Find E(Yn), V ar(Yn) and coefficient of variation of Yn1. If X and Y are random variables, find E[YE(X|Y=y)].If X₁, X2,..., Xn constitute a random sample of size n from an exponential population, show that X is a sufficient estimator of the parameter 0.
- 2. Let X be a random variable with E[X] = 15 and Var[X] = 10. Suppose Y = 2X – 7, Use the properties of E[ · ] and Var[ · ] to find the following: 2.1 E[Y] 2.2 Var[Y].If X is a Poisson variable such that P(X = 2) = 9P(X = 4) +90 P(X = 6), find the mean and variance of X.Show that E [ X – m]3 = E(X)3 - 3m, o? - m? where m, and o are the mean and variance of X respectively.
- For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))If X is a Poisson variable such that P(X =2) = 9P(X= 4) + 90P(X = 6), find the mean and variance of X.= B1. Let X₁ and Y; be random variables with Var(X;) = o² and Var(Y₂) o for all ie {1,...,n}. Assume that each pair (X₁, Y;) has correlation Corr(X, Y) = p, but that (X₁, Y₂) and (X₁, Y;) are independent for all i j. (a) What is Cov(X₁, Yi) in terms of Ox, Oy (b) Show that Cov(X₁,Y) = poxoy/n, where Y is the average of the Y₁. (c) Determine Cov(X, Y). and p?
