Question

3.In a lottery, you pick 4 digits (from 1-9) in order (the digits may be repeated). A lottery
ticket costs $1, and you win $5000 if your ticket matches the winning numbers. What is the
expected value of playing this lottery? What is the standard deviation of the relevant probability
distribution?

Answer 1

In the lottery, you pick 4 digits (from 1-9) .

Let X be the net profit or value of playing the lottery

Hence X=-1 if you lose and X=5000-1=4999 if you win.

Number of ways of choosing digit number using digits (from 1-9) is 9X9X9X9=6561

You win if the number chosen is same as 4 digit matching number.

Hence probability of winning lottery is 1/6561

Now the random variable X takes two values -1 and 4999 with probabilities 6560/6561 and 1/6561 respectively.

Therefore the random variable X has the probability mass function

Now, the expected value of playing this lottery is

Now to find the standard deviation

Hence

So the standard deviation of the relevant probability distribution is