# Question: If X and Y are jointly continuous with joint density

If X and Y are jointly continuous with joint density function fX,Y(x, y), show that X + Y is continuous with density function

## Relevant Questions

(a) If X has a gamma distribution with parameters (t, λ), what is the distribution of cX, c > 0? (b) Show that has a gamma distribution with parameters n, λ when n is a positive integer and χ22n is a chi-squared random ...Let X be a normal random variable with mean μ and variance σ2. Use the results of Theoretical Exercise 46 to show that In the preceding equation, [n/2] is the largest integer less than or equal to n/2. Check your answer by ...We say that X is stochastically larger than Y, written X ≥st Y, if, for all t. P{X > t} ≥ P{Y > t} Show that if X ≥st Y, then E[X] ≥ E[Y] when (a) X and Y are nonnegative random variables; (b) X and Y are arbitrary ...A certain region is inhabited by r distinct types of a certain species of insect. Each insect caught will, independently of the types of the previous catches, be of type i with probability (a) Compute the mean number of ...The k-of-r-out-of-n circular reliability system, k ≤ r ≤ n, consists of n components that are arranged in a circular fashion. Each component is either functional or failed, and the system functions if there is no block ...Post your question