Question
number 2.
Math 4030 Assignment #3 February 7, 2018 Name Show all work in a neat and organized manner pick three cards from a standard sheepshead deck. If they pick 3 trump, they are paid $40, if they 1. A player pays $12 to pick 2 trump they are paid $20, and if they pick 1 trump they are paid $10, otherwise they are paid nothing. What is the expected amount won (or lost) for each play of the game? 2 2. A certain discrete random variable X can only take on the values shown in the table. The probability mass function is shown in the table, compute f 3/A S/A 6/A 8/A 8/A 4/A 3/A 1/A F(x) a. the value of A b. cumulative distribution function for X c. P(4 X 13) d E(X), p(X) and (X) 3. An bag contains chips labeled with the numbers 4, 10, 16, 22, 184 a. If one chip is chosen at random from the bag what is the probability that the number on the chip is greater than 64? b If X is the value shown on a chip chosen at random, compute (X) and (X) 4. Suppose that in the manufacture of a certain type of candy bar a coupon for a free candy bar is randomly inserted into 4.2% of the wrappers. A distributor orders a shipment of 400 candy bars. a. What is the probability that there will be 20 or fewer coupons in the shipment?
Explanation / Answer
Solution
2) (a) Sum of f(x) = 1
So, 3/A + 5/A +....+1/A = 1
A = 38
(b) CDF : F(x) =
(c) P(4<x<=13) = P(X=6)+P(x=8)+P(X=9)+P(x=11)+P(X=13)
= 6/38+8/38+8/38+4/38+3/38 = 29/38
X 2 4 6 8 9 11 13 15 f(x) 3/38 5/38 6/38 8/38 8/38 4/38 3/38 1/38 F(x) 3/38 8/38 14/38 22/38 30/38 34/38 37/38 1
