Suppose Y (Y1, Y2, Y3)' ~ N(u, Σ) where (a) (b) = -6 2 fl= and Σ Find the distribution of = [2 130 1 1 Find the joint distribution of Z₁ = Y₁ + Y₂ + Y3 and Z2 = Y₁ - Y₂. (2) given Y3 = 1/2

Q: Let a r.v. have a mean of -1 and a standard deviation of 2. For the corresponding m.g.f. M(z), write…

A: mean =-1 and standard deviation =2 Then we have to find the generating function of z and it's…

Q: 9. If Y is distributed chi-square with 8 degrees of freedom. x²(9), find: e) K a value of y such…

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Q: 4. Suppose Y1, Y2 are independently and identically distributed with Unif((0,1)). Let Z = Y1 · Y2…

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Q: f(x) = c/x with x = 1,2,3. Given the Geometric Distribution find M(t).

A: Given, fx=cx,x=1,2,3 Consider,         ∑fx=1          ∑cx=1c1+c2+c3=1   c(1.8333)=1…

Q: distribution is given as X ~ U(0, 12). Find P(x > 3)

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Q: 3. Let y be distributed as N3 (μ, E) where (-²¹). 2 1 0 1 1 1 4. μ = Σ =|1 0 Find the distribution…

A: Objective of this question is that, find the distribution of Z , where Z given below Z=2Y1+3Y2-Y3

Q: 4. Find the expected values of ry 5. find the covariance Cov(X,Y) 6. find the correlation Cor(X,Y)

A: Expected value of xy: The expected value of xy can be calculated as: E[xy] = ∫∫ xy * f(x, y) dx dy…

Q: 7) Suppose the function Y have a hypergeometric distribution such that- N = 16, n = 5, k = 6 Find i)…

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Q: Establish a formula similar to (3.3.18. for the distribution. If X~ gamma (x,B) gamma then for any…

A: X is a Gamma random variable,γ(α,β) with PDF given as:

Q: Consider a mixture of two Gaussian distributions, [8.4 2 AN([12]. [6 %]) + 0.6N([8] · [²2* 1.7])…

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Q: Suppose that Y, and Y, are uniformly distributed over the triangle shaded in the accompanying…

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Q: Identify the distributions (and their parameters) whose moment-generating functions are given below.…

A: Moment Generating Function (MGF): The moment generating function (MGF) of a random variable X is…

Q: Find the mean and standard deviation for each uniform continuous model U(1, 13) U(70, 200) U(3, 92)

A: Obtain the mean and standard deviation for the uniform continuous model U(1,13). Obtain the mean of…

Q: Let X have a uniform distribution on the interval (0, 2). Given X = x, let Y have a (conditional)…

A: (a) The conditional pdf of Y given X = x is a uniform distribution on the interval (0, 0.5x), so:…

Q: x has the uniform distribution [0,1] put y=2x + 5 then y has the uniform distribution on the…

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Q: If X is a uniformly distributed random variable between -1 and 1 (pdf of x is constant=1/(2pi)…

A: From the given information, fx=12π, -π≤X≤π Given that Y=sin(X) Consider, the distribution function…

Q: 12) A metal bar is heated, and then allowed to cool. Its temperature T (in °C) is found to be The…

A: 12.) The temperature, T, at any time, t, is given as:T=15+75e−0.25tIt is required to find the rate…

Q: Solve: Let X ∼ Exp(λ), Y ∼ Exp(λ), and U ∼ Unif (0, 1). Find the distribution of U (X + Y ).

A: ANSWER: To find the distribution of U(X + Y), we can use the convolution formula for the probability…