Question

1.A pollster surveys 100 people and asks them how many hot dogs they eat monthly. The result is a discrete random variable that has the following probability distribution.

x	0	1	2	3	4	5
p(x)	0.15	0.58	0.15		0.04	0.02

(a)

Complete the missing value in the table.

x	0	1	2	3	4	5
p(x)	0.15	0.58	0.15		0.04	0.02

(b)

What is the median of this discrete random variable?

(c)

What is the mean of this discrete random variable?

(d)

Suppose the number of calories in a hot dog has a mean of 190 calories, and the bun contains, on average, 110 calories. Calculate the expected number of calories consumed each month due to eating hot dogs. Assume that every hot dog is consumed with a bun.

calories

2.The day after Thanksgiving, many people start shopping for Christmas. Suppose that a store was selling video games at a discount. The store limited the number of games a customer could purchase to four games. Let

x = number

of video games purchased, per customer. The associated probabilities are found in the table.

x	0	1	2	3	4
p(x)	0.01	0.04	0.10	0.31	0.54

(a)

What is the median of this discrete random variable?

(b)

What is the mean of this discrete random variable?

(c)

As an incentive, if a customer buys x video games they will receive x² "come-back dollars" which can be used to purchase items the next time they visit the store. What is the expected number of "come-back dollars" that will be received per customer on the sales of these games?

come-back dollars

Answer 1

a)as sum of all probabilities is 1

missing value =0.06

b)median of this discrete random variable =1 (as for x=1 , the cumulative proportion is 0.5)

c) mean =xP(X) =0*0.15+1*0.58+2*0.15+3*0.06+4*0.04+5*0.02 =1.32

expected number of calories consumed each month due to eating hot dogs =300*1.32 =396

2)

a) median =4

b)

mean =0*0.01+1*0.04+2*0.1+3*0.31+4*0.54 =3.33

c)

expected number of "come-back dollars" that will be received per customer on the sales of these games

=0²*0.01+1²*0.04+2²*0.1+3²*0.31+4²*0.54 =11.87