Transcript 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 .
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 Sn by 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. 𝑃[𝑋 = 𝑘] = 𝑞𝑘−1 𝑝
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?