2. Consider two sets of multivariate random variables: x = and y = (y₁, y2, ....ya)', where E[x] combined random vector: Z= (*) ) = (x1, x2, y' Suppose z~ Npq(μ, Σ), where μl: = f1 = ... and Σ : - (x1, x2, ‚xp)' .... ₁ and E[y] =₂. Let z be the ‚Xp, Y1, Y2, ..., Yq)' a. Show that x ~ Ν,(μι, Σπ) and y b. Show that x and y are independent Σ11 12 Σ21 Σ22 Ng(μ2, Σ22) if and only if Σ12 = Σ21 = 0

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A: X,Y ~ Uniform(0,2) E(X) = E(Y) = 0+22=1 Var(X) = Var(Y) = (2-0)212=412=13 Z = Yif X <122Yif X≥12…

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A: The answer can be given using the concept of normal distribution.

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A: Given that Y~Normal0,1 Here, E(Y)=0V(Y)=1⇒E(Y2)-EY2=1⇒E(Y2)-0=1⇒E(Y2)=1

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Q: 3- , thei a) E{f,(y\x)} =- exp(- o/27(2-r²) 20ʻ(2-r²)' 1 b) E{f, (x)f;(y)}=- 2.noV4-r

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A: Answer: Option (a)

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

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Q: iii) Show using the moment generating function technique that Y is a standard normal random…

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A: It is given that: varxi=σx2varyi=σy2 and xi and yi are independent and corrxi,yi=ρ

Q: i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and…

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Q: i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and…

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