Download - 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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7 sum of RVs
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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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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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7-3: 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
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7-4: sum of geometric RVs• Find the prob. generating function for a sum
of n independent, identically geometrically distributed random variables.
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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?