7 sum of RVs

7-1: variance of Z

• Find the variance of Z = X+Y by using Var(X), Var(Y), and Cov(X,Y)

7-2: iid RVs

• Find the mean and variance of the sum of n independent, identically distributed (iid) random variables, each with mean and variance 2 .

7-3: sum of Gaussian RVs

• Let Sn be the sum of n independent Gaussian random variables with re-spective means m1, …, mn, and 1

2, …, n

2

• Find the pdf of Sn by using characteris-tic function

7-4: sum of geometric RVs• Find the prob. generating function for a sum

of n independent, identically geometrically distributed random variables.

7-5: central limit theorem• Suppose that orders at a restaurant are iid

random variables with mean ($8) and stan-dard deviation ($2).

• Estimate the probability that the first 100 cus-tomers spend a total of more than $840.

• Estimate the probability that the first 100 cus-tomers spend a total of between $780 and $820.

• After how many orders can we be 90% sure that the total spent by all customers is more than $1000?