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…

Q: Q1. Suppose that X and Y are jointly continuous random variable - x for 0 < x < 1 and 1 < y < 2 f(x,…

A: As per our company guidelines we are supposed to  answer only first 3 subparts. kindly repost other…

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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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A: *answer:

Q: 2. Let Z1,..., Z, be i.i.d. standard normal random variables and define X = Z;, k = 1,..., n. j=1…

A:

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A:

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

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

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Q: and let Y; = Xí, i = 1, ..., n. %3D Find the distribution of W 2(Y1+Y2+Y3) 3(Y4+Y5)

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Q: i) State, with parameter(s), the probability distribution of the statistic, T = 2 54 ₁² 211 212 iii)…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted

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Q: 0, x)

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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…

A: It is given that  X follows N(θ, 1), then E(X) = θ and V(X) = 1, And the moment genarating function…

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