Let Y denote a binomial random variable with n trials and probability of success p. Find the probability-generating function for Y and use it to find E(Y) and V(Y).
a) G_Y (t)=(1−p+pt)ⁿ ; E(Y)=np, V(Y)=np(1−p)
b) G_Y (t)=(1+p-pt)ⁿ ; E(Y)=np, V(Y)=np(1+p)
c) G_Y (t)=(1−p-pt)ⁿ ; E(Y)=np, V(Y)=np(1−p)
d) G_Y (t)=(1+p+pt)ⁿ ; E(Y)=np, V(Y)=np(1+p)