1.) Find the value ofkfor which the given function is a probability density function.

f(x) =2k

on[1, 1]

2.)Find the value ofkfor which the given function is a probability density function.

f(x) =ke^kx

on[0,8]

3.)Your company's new series "Avocado Comedy Hour" has been a complete flop, with viewership continuously declining at a rate of35%per month. Use a suitable density function to calculate the probability that a randomly chosen viewer will be lost sometime in the nextthreemonths. (Round your answer to four decimal places.)