6. Given a continuous uniform distribution, show that A+B (a) μ and 2 (b)σ2 (b) σ² = (B-A)² 12
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- Let X ∼ N(2, 4). (a) What is the distribution of (X−2) /2 ?Let X = b(16,- find E(4- 3x) and distribution function.Prove that the mean and variance of a uniform distribution are respectively given by E(X) = (a + b)/2 and Var (X) = (b – a) 2/12, where aand b are respectively the lower and upper limits of the distribution.
- Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.Let Y₁,..., Yn be an iid sample U(0, 0), 0 > 0, with pdf { 1/0, 0≤ y ≤0, 0, elsewhere and CDF f(y) = F(y) = = 0, y < 0, y/0, 0≤ y ≤ 0, 1, y ≥ 0Suppose that X has the uniform distribution on the interval [0, 1]. Compute the variance of X.