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) Find p by integrating the joint density function over the appropriate region. (b) Find p by using the fact that all 4! possible orderings of X1, . . . , X4 are equally likely. [Difficulty] I have starting problem with (a) (b) seems to be easy [Thoughts] For (b), X1 __ X2 __ X3 __ X4 The symbols can be arranged in 4! ways. The signs in each blank can be either <, = or >= The blanks need to be filled with <, > and < respectively, SO, P(<) = P(>) = P(=) = 1/3 So (b) must be (1/3)^3 times 4!
