Random variables with a common distribution function

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1. Suppose that X and Y are independent binomial random variables with parameters (n, p) and (m, p). Argue probabilistically (no computations necessary) that X + Y is binomial with parameters (n + m, p).

2. Let X1, X2, X3, and X4 be independent continuous random variables with a common distribution function F and let p = P{X1 <>X2 > X3 X4}

(a) Argue that the value of p is the same for all continuous distribution functions F.

(b) Find p by integrating the joint density function over the appropriate region.

Reference no: EM131005635

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