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7 sum of RVs

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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  1. 7 sum of RVs

  2. 7-1: variance of Z • Find the variance of Z = X+Y by using Var(X), Var(Y), and Cov(X,Y)

  3. 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 .

  4. 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

  5. 7-4: sum of geometric RVs • Find the prob. generating function for a sum of n independent, identically geometrically distributed random variables.

  6. 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?

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