How to determine distribution with no parameters

#1
I'm confused by this question and I was hoping for some guidance some one to point me in the right direction

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)
 

BGM

TS Contributor
#2
Do you know the (name of the) distribution of those \( Y_i \)?

Are they i.i.d.?

Do you know the distribution of the sum of i.i.d. rvs from such distribution?