Question

In a statewide lottery, one can buy a ticket for $1. With probability .0000001, one wins a million dollars ($1,000,000), and with probability .9999999 one wins nothing ($0). Let Y denote the winnings from buying one ticket. Construct the probability distribution for Y. Show that the mean of the distribution equals .10, corresponding to an expected return of 10 cents for the dollar paid.

Answer 1

Using the expected value, it is found that the mean of the distribution equals $0.1.

• The expected value, which is the mean of the distribution, is given by each outcome multiplied by it's probability.

The probabilities of each outcome are:

• .0000001 probability of earning $1,000,000.
• .9999999 probability of earning $0.

Thus, the mean is given by:

$E(Y) = 0.0000001(1000000) + 0.9999999(0) = 0.1$

Thus showing that the expected value is $0.1.

A similar problem is given at brainly.com/question/24855677