Q3: Let X₁, X2, ......., Xn be i.i.d from Gamma distribution (x~ GAM( e, 3), show that s= sufficient for e (HINT Σx, ~ GAM (0, 3n))

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Q: Let x~ exp (A) Show that T=s Xi is sufficiency Statistic.

A: Generally we use factorization theorem to obtain the sufficient statistic.

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Q: Page 327, 5.1.7.* Let X₁, ...,Xn be iid random variables with common pdf f(x) exp{-(x-20)}, x > 20,-…

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Q: 6. Suppose Y = (1, 2, 3)' ~ N(μ, 2) where -4 (a) (b) and E=1 3 0 Find the joint distribution of Z₁ =…

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Q: 3. Let X1,..X be a random sample from f(r, 0) =, 0 0. Let Y1 = min,{X,}. Find consistent estimators…

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Q: 2. Let Y₁,..., Yp be independent random variables such that Y~ N(0, 1). Write Y = (Y₁...., Yp) and 0…

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Q: 3. Suppose X and Y are two independent Gamma random variables: X~ Y Gamma(2, B = 1), where the first…

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Q: Suppose that X and Y are independent, X~B(10, 0.5), Y follows Poisson distribution with parameter 4.…

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Q: (4x Q2. Let f(x) = { 4(1 – x) 1/2 3/4) c) Find the probabilities given in part (b)

A: f(x) = 4x  , 0 ≤x≤1/2           4(1-x) , 1/2 ≤x ≤1

Q: 4), X2 ∼ N(μ = 1, σ^2 = 16), and X3 ∼N(μ = −4, σ^2 = 9). Let X1, X2, and X3 be independent and Y =…

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

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Q: Pixels of an image r- fi(x,y) take integer values r € (0,1,. 255}). Their histogram is estimated as:…

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