Consider a bettering game where you bet $10 and have a probability of 0.45 of getting $20 back ($10 more than you started with) and a probability of 0.55 of getting no money back (losing the initial $10). The net amount of money gained on each trial is a discrete random variable. Note that losing money can be expressed as a negative gain.

(a) Draw a probability mass function representing this random variable.

(b) Find the expected value of this pmf.

(c) If you start with $50, what is the expected amount of money to be left with after playing 20 times?

(a)

(b)

-1

(c)

30

Step-by-step explanation:

(a)

Your random variable will have two possible values, 30 and 0, one of them with a probability of 0.45 and the other one with a probability of 0.55. Therefore it looks like this.

(b)

The expected value of this PMF would be

therefore on average you will have a dollar less.

(c)

For this one, if you play 20 times and your initial amount is 50$ then you have to compute the following expectation.

answer: 80,000

step-by-step explanation:

the population doubles every day.

10,000*2=20,000 day 4

20,000*2=40,000 day 5

40,000*2=80,000 day 6