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.

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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?


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