Question

1.

Create a PDF table and calculate expected value.

A friend offers you a game to play where you pay him $10. You roll a fair 6-sided die. If the roll of a comes up as 1, 2, 3 he pays you $5. If the roll is 4 or 5 he pays you $7 and if it is a 6 he pays you $20.

In words, define the random variable X. ?

Construct a PDF table.

If you play this game many time, what would your expected average winnings/losses be? ?

2.

Create your own Binomial Probability RV and Distribution

4. Describe your Binomial Experiment. Choose an n of between 20 and 100:

5. Success = __________________________   Failure = _____________________________

6. X ~ _____ (______, ______)

7. List or give the range of the values that X takes on:

8. Give the PDF formula for the RV:

9. Find the expected value and standard deviation for your random variable.  

10. Write the probability questions described below about YOUR binomial RV and evaluate the probabilities.

a. A probability that X = a single value

b. A probability with “at most”

d. A probability with “more than”

e. A probability with "between"

Answer 1

(1)

The pdf for this function is as shown below:

Here X denotes the money that is earned according to the number that comes up on the die when it is rolled.

Number on die	1	2	3	4	5	6
X	5	5	5	7	7	20
P(X)	1/6	1/6	1/6	1/6	1/6	1/6

So the expected money which is earned from this game is:

E[X] = (5+5+5+7+7+20)/6 = $8.167

Amount paid to play the game = $10

So the expected losses from this game = 8.167-10 = - $1.833

The -ve sign here shows that loss has occurred.