6. Suppose Y = (Y₁, Y2, Y3)' ~ N(μ, Σ) where E) (a) (b) f [2 1 11 and Σ = |1 3 0 10 2 Find the joint distribution of Z₁ = Y₁+Y₂+ Y3 and Z₂ = Y₁ - Y₂. Find the distribution of given Y₁ = 1/2

Q: please give me answer in relatable

A: we decompose the total variance into within-group and between-group variances ,showing they sum to…

Q: Let (x1, x2, ..., xn) be independent samples from the uniform distribution on [0, θ]. Let X(n) and…

A:

Q: 4. Capture-recapture. A population of b animals has had a number a of its members captured, marked,…

A:

Q: Let X have a Poisson distribution with a mean of 3. Define Y = (X-3) ^2 , specify pdf from Y.

A: Note: According to Bartleby expert guidelines, we can answer only first question with their three…

Q: Suppose that Y1,..., Yn is a sample of size n from a Exp(B), B > 0. .3B (a) Find the distribution of…

A:

Q: 3. Let X be a random variable that is uniformly distributed on the interval (a, b). Find its moment…

A: Moment Generating Function for a random variable X is given by,  E(etX) = ∫-∞∞etxf(x) dx where f(x)…

Q: 3- Suppose that X and Y are independent and X,Y~ N(0,0²). Show that U and V are independent with…

A: Suppose W, Z ~i.i.dN0,1.  The joint probability distribution of W and Z can be written as follows:…

Q: Let X ~ N(0,1), the standard Normal distribution. (a) Determine the 3rd moment of X. (b) Determine…

A:

Q: If(x,y)-N(0-11,4,0.5),the marginal distribution of X~ Y₂

A:

Q: 10. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and…

A: The objective of this question is to find the joint and conditional probability density functions of…

Q: (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer…

A: Let X be the random variable that the time headway.  The pdf of X is,  f(x)=11x12, x>1 The cdf of…

Q: X = N(u₂o N(μ, o²), let Let Y = 2X+b, b0, then distribution of Y is

A:

Q: 12. The first four central moments of distribution are 0, 2.5, 0.7 and 18.75. Comment upon the…

A:

Q: Let X = ((X,,Y),....(X, Yn)) be a sample from a bivariate normal population. how that the…

A: Given information: It is given that X be a sample from a bivariate normal population.

Q: (a) Let X1 ~ x² (n, 8) and X2 ~ x² (m, 1). mX1 and its parameters. nX2 (i) Find the distribution of…

A:

Q: Suppose we collect n samplesX1,X2, . . . ,Xn from a uniform distribution U[θ,1]. We know the maximum…

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

Q: Let x1, X2, ..., Xn be a random sample from a continuous uniform distribution with domain (0,b).…

A: Here,  Given that,x~U(0,b)fx(x)=1b, 0<x<b0    otherwise