We have n = 100 many random variables xi 's, where the xi 's are independent and identically distributed bernoulli random variables with p = 0.5 (e(xi)=p and var(xi)=p(1- a. what distribution does pn i=1 xi follow exactly (sum bernoulli random varaibles)? state the type of distribution and what the parameter is

Recall that for a random variable following a Bernoulli distribution , we have the moment-generating function (MGF)



and also recall that the MGF of a sum of i.i.d. random variables is the product of the MGFs of each distribution:



So for a sum of Bernoulli-distributed i.i.d. random variables , we have



which is the MGF of the binomial distribution . (Indeed, the Bernoulli distribution is identical to the binomial distribution when .)