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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.Suppose f(x)=3x2, 0<x<1 is a density function of X. Find P(1/2<X<2).8. Show that the gamma density function f(x, λ, r) integrates to 1
- 5.) Suppose the joint density for X and Y is given by f(x, y) = 1/xfor 0 < y < x < 1. Find ρX,YIf X is uniformly distributed over (0,1), find the density function of Y = eXSuppose 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)?
- Can the following be a density function (give reasons):f(x, y) = ce−(2x2+6xy+3y2), −∞ < x < ∞, −∞ < y < ∞where c is a positive constant.Let y1, y2,.., y10 be a random sample from an exponential pdf with unknown parameter A. Find the form of the GLRT for Ho : = ^o versus H1 : A ± do. What integral would have to be evaluated to determine the critical value if a were equal to 0.05?Suppose X and Y have joint density f(x,y)=10x2y, 0<y<x<1. Find the marginal density of X.