# 7 sum of RVs - PowerPoint PPT Presentation

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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.

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7 sum of RVs

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## 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 respective means m1, …, mn, and 12, …, n2

• Find the pdf of Snby using characteristic 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 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?