fxkcosx for x between 0 and 2 0 otherwise a For what value o

f(x)=kcos(x) for x between 0 and /2, 0 otherwise

a) For what value of k is this a pdf?

    b) Find F(x)=P(X<x) as a function of x.

    c) What is the probability X is between 0.25 and 0.62?

    d) What value of x is the 82^nd percentile?

    e) Find E(X).

    f) Find Var(X).

Solution