1. Graphed, their distribution had a shape similar to the probability density function

fX(x) = (1)/(C \sqrt(84-x)), 20<= x<= 80

0 elsewhere

(a) Find a value of C that makes fX(x) a valid probability density function.

(b) Find the cumulative distribution function of X, FX(x) = P ( X<= x).

"Hint": To double-check your answer: should be FX(20) = 0 , FX(80) = 1.

2. Consider a discrete random variable X with the probability mass function

PX(x) = 2x+3/16, x = -1,0,1,2

0 elsewhere

Consider Y =g(x)=4-X^2

Find the probability distribution of Y.