a) Show the this function as density possibility like proof b)find the median value
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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.The random vector (X, Y)' has a probability density:f(x,y) = 1/8(3xy2 + x); where x bellongs to interval <0;2> and y bellogns to interval <-1;1> = 0 ; otherwise Count the F(3/2; 0) Please be more specific in solution, so I can better understand the topic.Thanks!Find the density of Z = X-Y for independent Exp(λ) random varibles X and Y. Show all Work!!
- A random variable is called a power law random variable ifP(X > t) = max{1/(t^α), 1}for some α. What is the density of X? Compute the mean of X when α > 1. What happens if α < 1?Let X and Y be independent and exponential with parameter lambda. Show that the density of X conditional on X+Y=v is uniform on [0,v]Assume that X and Y are jointly continuous random variables with joint probabilitydensity function given by A. Find the marginal density functions for X and Y . B. Find E[X] and E[Y ]. C. Find Cov(X, Y ).
- Let X and Y be two random variables with joint density function f(x,y) = (3 − x + 2y) / 60, for 1 < x < 3, 0 < y < 5. Find the marginal density functions. (Check that they are nonnegative and integrate to 1 before continuing further) Are X and Y independent? Explain.Randomly choose a number X from the density f X ( x ) = x 8 for 0 ≤ x < 4 (and zero otherwise). If X < 2, toss a fair coin twice. Otherwise toss the coin once. Let N be the number of tails and let Y = X+N. Find P ( X < 2 | Y > 2.5 ).A continuous random variable X is defined by f ( x ) = (3+x)^2/16 ; -3<x<-1 f(x) = = ( 6 - 2x^2)/16 ; -1<x<1 f(x) = ( 3 - x^2)/16 ; -1<x<3 a. Verify that f(x) is density b. find the mean
- A VA X has a probability density f (x) = 3x² in the interval [0.1]. Determine F (x) = p (xA student has 3 volumes of short stories and 2 novels on a bookshelf. She selects 3 books at random to take home over vacation. A random variable X is defined to be the number of novels selected. Find the values assumed by X and its density function.If X has the uniform density with the parameters α = 0and β = 1, use the distribution function technique to findthe probability density of the random variable Y = √X.