Let's consider r.v.s X and Y and a continuous bivariate distribution f(X,Y) defined by f(x, y) = { 3.x 0 for0≤y≤x≤1 otherwise a.) Find the marginal distribution of X. b.) Find the marginal distribution of Y. c.) Find дx and Var(X) d.) Find #y and Var(Y) e.) Find Cov(X,Y) f.) Define Z = 2X – Y. Find E(Z) and Var(Z)
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- Let X = b(16,- find E(4- 3x) and distribution function.Let X have a uniform distribution on the interval (4, 10). Find the probability that the sum of 2 independent observations of X is greater than 19.Let X have a uniform distribution on the interval (7, 12). Find the probability that the sum of 2 independent observations of X is greater than 23.Consider X ∼ Unif(0, 1), and find the distribution of Y = 1/X.
- Solve: Let X ∼ Exp(λ), Y ∼ Exp(λ), and U ∼ Unif (0, 1). Find the distribution of U (X + Y ). Please don't handwriting solutionLet 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 ≥ 0If X and Y are two independent uniform distribution with X(0 ,4) and Y(0,6). Find the joint pdf f (x.y). Find P(2.5<X<3.5,1<Y<4)