Let X1 ~ x² (n, 8) and X2 ~ x² (m, 2) : mX1 find the expected value of X = nX2 Е (X).

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A: Formula used Var ( X+Y) = Var(X)+Var(Y)+2Cov(X,Y)

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A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

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Q: (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X.

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A: Generally we use factorization theorem to obtain the sufficient statistic.

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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: Prove that the variance of b, V(b) = o²(X'X)−¹

A: Given that We have to show that Var(b)=σ2(X'X)-1

Q: (1) Let X = b(16,) find E(4-3x) and distribution function.

A: From the provided information, X~b (16, 1/4) Sample size (n) = 16 Probability (p) = 1/4

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A: The joint probability distribution of X and Y is given by:

Q: 4, ELY Suppose X and Y are two random variables with E[X] = 1, Var (X) Var (Y) = 4, and Cov (X, Y) =…

A: Var(X)=4, Var(Y)=4, Cov(X,Y)=1

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Q: and another random variable Y = 2X. Then find (a) value K, (b) E[X], (c) E[Y] and (d) E[XY].

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Q: Q4)The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.

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Q: Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is

A: From the given information, the joint density function for X  and Y is,