Let X and Y be two independent random variables, X ∼ Γ(α, λ) and Y ∼ Γ(β, λ). Find the joint probability density function f(Z,W)of the vector (Z, W) (b) Show that Z and W are independent (c) Show that Z ∼ Γ(α + β, λ) and W ∼ B(α, β)
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Let X and Y be two independent random variables, X ∼ Γ(α, λ) and Y ∼ Γ(β, λ).
Find the joint probability density
(b) Show that Z and W are independent
(c) Show that Z ∼ Γ(α + β, λ) and W ∼ B(α, β)
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- Let X be a continuous random variable with probability density function 1 -1sxs1 fx(x) = { 2 0 else The value of P(X´ > 2) is Select one: а. 1 b. 1/2 c. 0.707 d. 0.293 е. Оb) Let Z₁ = X-XN (0,1), and W₁ dx YHY~N(0,1), for i = 1,2,3,...,10, then: dy i) State, with parameter(s), the probability distribution of the statistic, T = - 54 1² ii) Find the mean and variance of the statistic T = Σ},wp? Σ1,2,3 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of ẞ such that P(T> B) = 0.01, where T = Σ₁Z₁² + ₁ W₁².The density function of two random variables X and Y is ,-2(x+y) fx,r (x, y) =u(x)u(y)4e¯¾x*y) X,Y Find the mean value of the function e-*+),
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