STAT 10 Prof. Elsdon spring 2018 Rev. Name: Some Discrete Distributions ssignmen
ID: 3355254 • Letter: S
Question
STAT 10 Prof. Elsdon spring 2018 Rev. Name: Some Discrete Distributions ssignment # 8 Class Days& Start Time: 1) (a) Find the missing probability, the mean, the standard deviation, and the variance of the given probability distribution. Round the variance and standard deviation to two decimal places. XP(X) -20 0.45 2 0.12 5 0.20 the missing probability: mean:- standard deviation : variance 20 (b) Suppose that the X in this distribution is the net amount of dollars that I win each time I play a certain gambling game. Would it be wise for me to play this game over and over for a long period of time? Give a good explanation that supports your answer 2) A certain gambling game involves rolling a pair of fair dice. Suppose the rules for this game are as follows: The player has to pay S5 for each roll of the dice. If a two, three, or a twelve is rolled then the player is given $16. If a six or an eight is rolled then the player is given S8. If a seven or an eleven is rolled then the player is given $2. If any thing else is rolled then the player is not given any money. Let the random variable X be the net winnings for the player each time the dice are rolled. a) Make a probability distribution for X by filling in the table. b) Find the mean of X. c) Find the standard deviation of X X P(X) d) Is it wise for the player to play this game over and over for a long period of time? Give a good explanation. e) How much can the player expect to win or lose if he plays 500 times? Is this amount a "win" or a "loss"?Explanation / Answer
Question 1
Missing probability = 1 - (0.45 + 0.12 + 0.20) = 0.23
Mean = -20 * 0.45 + 2 * 0.12 + 5 * 0.20 + 20 * 0.23 = -3.16
Variance = 0.45 * (-20 + 3.16)2 + 0.12 * (2 + 3.16)2 + 0.20 * (5 + 3.16)2 + 0.23 * (20 + 3.16)2 = 225.0935
Standard deviation = sqrt(225.0935) = 15.00312
(b) Here as the expected income from one game is $ -3.16 so it would not be wise to play game over and over as that in long run it would produce negative return.
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