Question

Prizes and the chances of winning in a sweepstakes are given in the table below.

Answer 1

The expected value of the discrete distribution, for each case, is given as follows:

a) Amount won by one entry: $0.075.

b) If the cost is the cost of a postage stamp:  -$0.525.

How to obtain the expected value of a discrete distribution?

The expected value of a discrete distribution is obtained with the sum of each outcome multiplied by it's probabillity.

In this problem, the distribution for the prizes is given as follows:

• P(X = 10,000,000) = 1/300,000,000.

• P(X = 350,000) = 1/150,000,000.

• P(X = 50,000) = 1/10,000,000.

• P(X = 20,000) = 1/1,000,000.

• P(X = 400) = 1/200,000.

• P(X = 75) = 1/6,000.

Hence the expected value for the prizes is:

E(X) = 10,000,000 x 1/300,000,000 + 350,000 x 1/150,000,000 + 50,000 x 1/10,000,000 + 20,000 x 1/1,000,000 + 400 x 1/200,000 + 75 x 1/6,000 = $0.075.

The cost of a postage stamp is of $0.6, hence the expected value considering this cost would be of:

0.075 - 0.6 = -$0.525.

More can be learned about the expected value of a discrete distribution at brainly.com/question/27899440

#SPJ1