1a.) Consider a random variable X whose density is:

f(x) = ax + bx^2 for x in [0,1], and 0 otherwise. If E[X]=.6, find a and b. For the above X, find Var(X).

b.) Find c such that f(x)=c(1/3)^x is the pmf of a discrete random variable.

c.) What kind of random variable is the random variable X having the above pmf?

d.) For the above X find P(X>7).

e.) For the above X find its mgf.