Hey guys, I have a couple problems I am trying to work out. I am quite unsure on how to solve them.
1. Let pi = P{X = i} and soppose that p1 + p2 + p3 = 1. If E[X] = 2, what values of p1,p2,p3
a) maximize Var(X)
b) minimize Var(X)
I have:
a) you have to take the derivitive but i dont know of what....
I have:
1/3(p1)^2 + 1/3(p2)^2 + 1/3(p3)^2 - 4 = 0
Then
(p1)^2 + (p2)^2 + (p3)^2 = 12
Do I take the derivative with respect to each p1,p2,p3? In that case, the answer would be 0?
b) What do I do to minimize?
2. A community consists of 100 married couples. If during a given year 50 of the members of the community die, what is the expected number of marriages that remain intact? Assume that the set of people who die is equally likely to be any of the (200 over 50) groups of size 50. (Hint: For i = 1,....100 let
Xi = 1 if neither member of couple i dies
0 otherwise.
P{Xi = 1} = 1/n
E[X] = E[Xi]+...+ E[Xn] = (1/n)n = 1
Thats all i have for that one.....
Any help is appreciated. Thank you!
1. Let pi = P{X = i} and soppose that p1 + p2 + p3 = 1. If E[X] = 2, what values of p1,p2,p3
a) maximize Var(X)
b) minimize Var(X)
I have:
a) you have to take the derivitive but i dont know of what....
I have:
1/3(p1)^2 + 1/3(p2)^2 + 1/3(p3)^2 - 4 = 0
Then
(p1)^2 + (p2)^2 + (p3)^2 = 12
Do I take the derivative with respect to each p1,p2,p3? In that case, the answer would be 0?
b) What do I do to minimize?
2. A community consists of 100 married couples. If during a given year 50 of the members of the community die, what is the expected number of marriages that remain intact? Assume that the set of people who die is equally likely to be any of the (200 over 50) groups of size 50. (Hint: For i = 1,....100 let
Xi = 1 if neither member of couple i dies
0 otherwise.
P{Xi = 1} = 1/n
E[X] = E[Xi]+...+ E[Xn] = (1/n)n = 1
Thats all i have for that one.....
Any help is appreciated. Thank you!