1. ## Find E(X)

In a state lottery a three digit integer is selected at random. A player bets $1 on a particular number and if that number is selected, the payoff is$500 minus the $1 paid for the ticket. Let X equal the payoff to the bettor, namely -$1 or $499, and find E(X). 2. Originally Posted by jennifer1004 In a state lottery a three digit integer is selected at random. A player bets$1 on a particular number and if that number is selected, the payoff is $500 minus the$1 paid for the ticket. Let X equal the payoff to the bettor, namely -$1 or$499, and find E(X).
The numbers start from 001 and end at 999. So there are 999 numbers.

Therefore Pr(X = -1) = 998/999 and Pr(X = 499) = 1/999.

Calculate E(X) in the usual way.

3. Is E(X) then (-1*999)+(499*1)=499-999 = -500? Thank you for your help.

4. Originally Posted by jennifer1004
Is E(X) then (-1*999)+(499*1)=499-999 = -500? Thank you for your help.
No, the expected pay off is:

(-1)Pr(-1)+(499)Pr(499)=-1(998/999)+499(1/999)

and a simple reality check should tell you that the expected pay-off is of the order of -0.5.

Also the wording of the original problem is vague and inplausible so double check it.

CB

5. That is the way the problem is worded. All problems in my text seem to be vague. Would the pribabilities actually be 999/1000 and 1/1000 since 0 0 0 would also be considered a three digit integer? This would then make E(X)=-1/2 rather than -.4995

6. Originally Posted by jennifer1004
That is the way the problem is worded. All problems in my text seem to be vague. Would the pribabilities actually be 999/1000 and 1/1000 since 0 0 0 would also be considered a three digit integer? This would then make E(X)=-1/2 rather than -.4995