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)

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Presentation transcript:

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 S n be the sum of n independent Gaussian random variables with respective means m 1, …, m n, and  1 2, …,  n 2 Find the pdf of S n by using characteristic function

7-4: sum of geometric RVs

7-5: central limit theorem Suppose that orders at a restaurant are iid random variables with mean  ($8) and standard deviation  ($2). Estimate the probability that the first 100 customers spend a total of more than $840. Estimate the probability that the first 100 customers 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?