Question

A fair die is rolled 100 times. Let X add the faces of all of the rolls together. Then µ = 350. Find an upper bound for P(X ≥ 400). Find the actual probability P(X = 100)

Answer 1

from Markov' INequality P(X>=a) <=E(x)/a

therefore upper bound for P(X ≥ 400) =350/400=7/8

since for X =100, each roll outcome should be 1

therefore P(X=100) =(1/6)¹⁰⁰