Thread: Distribution Functions

Let X and Y be independent and identicall distributed random variables. Denote their common probability distribution function by F and denote their common density function by f. If

V = max{X,Y} and U = min{X,Y}

1.Express the distribution function of V in terms of F and f.

Hint: Begin with Fv(v) = P[V<=v]

2. Express the distribution function of U in terms of F and f.

Note that if V < v, both X and Y must be less than v.



Do the same for U. (begin with P(U > u))

Thanks, for that

so does that mean that its
F(u) = P(U>u) = P(X>u, Y>u) = P(X>u)P(Y>u) = [f(u)]^2

No. The cumulative distribution function is defined as .
Note that, since P is a probability, .

See you!