How Do You Calculate the Standard Deviation of Profit Per Lottery Ticket?

[koudai8]

[solved]Expected Value and Variance

Hi, I have a problem on Expected Value and Variance, and having spent hours but still couldn't figure out :(

One state lottery has 200 prizes of $1
100 prizes of $5
40 prizes of $25
13 prizes of $100
4 prizes of $350
1 prize of $1000
Assuming that 17,000 lottery tickets are issued and sold for $1

1. what is the lottery's expected profit per ticket

For this problem, I solved it two ways. First by summing the [products of all the numbers of tickets with their payouts], which is 5400 then (17000-5400)/17000 to get $0.6824
Second way by summing the [product of the payouts of tickets with their probabilities] = $0.6824

Having explained what I did for the first problem, here is the "real" problem:

2. What is the lottery's standard deviation of profit per ticket?

Since I found the answer to the expected value indirectly, I'm a blind goose in a hailstorm on number 2...

 

[chiro]

Hi, I have a problem on Expected Value and Variance, and having spent hours but still couldn't figure out :(

One state lottery has 200 prizes of $1
100 prizes of $5
40 prizes of $25
13 prizes of $100
4 prizes of $350
1 prize of $1000
Assuming that 17,000 lottery tickets are issued and sold for $1




Having explained what I did for the first problem, here is the "real" problem:



Since I found the answer to the expected value indirectly, I'm a blind goose in a hailstorm on number 2...

Hey kuodai8 and welcome to the forums.

When you are you asking questions on the forums, you need to show some working out before helping you. (It's the forum policy and it's intended to help the poster so that they progress more independently, but you will find PF is a pretty supportive place for help).

So I will start you off by asking you the following:

How do you define the random variable that represents profit?

 

[koudai8]

Hey kuodai8 and welcome to the forums.

When you are you asking questions on the forums, you need to show some working out before helping you. (It's the forum policy and it's intended to help the poster so that they progress more independently, but you will find PF is a pretty supportive place for help).

So I will start you off by asking you the following:

How do you define the random variable that represents profit?

Hi, I've solved it already. I defined profit by [(-1)+1]+[(-5)+1]+[(-25)+1]+[(-100)+1]+[(-350)+1]+[(-1000)+1]+1