Let X1.........Xn be a random sample from a population with mean μ, that is E(Xi)=μ for all 1≤i≤n. Define

Yi=1 if Xi<μ and Yi=0 otherwise

a) Determine the distribution of Y=∑1≤i≤nYi (name and parameters)

b)Determine the mean and variance of Y

c)Compute P(Y≤30) for special case of n=49 and Xi..........Xn iid Exp∼(λ=3)