1. Create a PDF table and calculate expected value. A friend offers you a game t
ID: 3368678 • Letter: 1
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"
Explanation / Answer
(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
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.
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 1/6Related Questions
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