3.6.1 Summation of Random Variables

Question 1

what does it mean that variables are independenty and identically distributed?

Answer 1

it means that all variables follow the same distribution and are independent of each other?

Question 2

how should you treat the expectation of the sum of iid variables?

Answer 2

variance is the same story since both are linear operators

Question 3

what distrubition does the sum of n brenoulli’s follow?

Answer 3

binomial(n,p)

Question 4

what distrubition does the sum of geometric follow?

Answer 4

negative binomial(r = n, p)

Question 5

what distrubition does the sum of poissons follow?

Answer 5

also poisson(nλ)

Question 6

what distrubition does the sum of exponentials follow?

Answer 6

gamma(α = n, θ)

Question 7

what distrubition does the sum of normals follow?

Answer 7

also normal with (nμ, nσ^2)

Question 8

what does it mean that random variables are Independent but Not Identically Distributed

Answer 8

they are independent but don’t follow the same distribution?

Question 9

how should you treat the expectation and variance of the sum of independent but not indentically distributed variables?

Answer 9

expectation is the same story

Question 10

how should you treat the expectation and variance of a linear combination of random variables?

Answer 10