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- Suppose that X has the density function c(x) = CX2 for 0 ≤ x ≤ 1 and f(x) = 0 otherwise.a. Find c.b. Find the cdf.c. What is P(.1≤ X <.5)?Compute E[X] if X has a density function given byLet Y possess a density functionf (y) =c(2 − y), 0 ≤ y ≤ 2, 0, elsewher Find c.b Find F(y).c Graph f (y) and F(y).
- Can the following be a density function (give reasons):f(x, y) = ce−(2x2+6xy+3y2), −∞ < x < ∞, −∞ < y < ∞where c is a positive constant.1. Let f (x) = cx 3 and S X = [0, 2] (X is continuous and c is a constant). a. What value of c will make f (x) a valid density?b. What is P (X = 1)?c. What is P (X = 1 or X = 2)?5.) Suppose the joint density for X and Y is given by f(x, y) = 1/xfor 0 < y < x < 1. Find ρX,Y
- If X is uniformly distributed over (0,1), find the density function of Y = eXLet x denote the amount of time for which a book on 2-hour reserve at a college library is checked out by a student, and suppose that x has density func- tion f(x)5.5x for 0,x,2.8. Show that the gamma density function f(x, λ, r) integrates to 1