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

Q: Suppose that Y ~ Normal(0, 1) and define new random variable X by X=Y². Compute ELYI

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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A:

Q: 29.- Let X1, X, be a random sample from the population with distribution N(0, 1). Obtain the…

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A: The problem can be solved using the concept of expectation and moment generating function.

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A: The distribution is given by, fX(x) = xe-xx>00Otherwise So,  P(X≥x)=∫x∞fX(t) dt=∫x∞te-t…

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A: We have given the following statement.

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A:

Q: 0, x)

A: a) The required value is calculated as follows: fx=ddxFx      =ddxx24     =2x4     =x2…

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A:

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A: In this problem, we are dealing with independent random variables  with a given density function…