Question

1. This problem has two parts. BUT the second part will appear ONLY AFTER you have answered the first part correctly.)

Rework problem 9 in section 4.2 of your text, involving a defective vending machine. Assume that the machine yields the item selected 70 percent of the time, and returns nothing 30 percent of the time. Three individuals attempt to use the machine. Let XX be defined as the number of individuals who obtain the item selected.

2.

Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 18 markers: 13 that contain ink and 5 that do not contain ink. A sample of 7 markers is selected and a random variable YY is defined as the number of markers selected which do not have ink.

How many different values are possible for the random variable YY?

Fill in the table below to complete the probability density function. Be certain to list the values of YYin ascending order.

How many different values are possible for the random variable XX?

3.

Fill in the table below to complete the probability density function. Be certain to list the values of XXin ascending order.

Answer 1

1. ans

XX = i, i = 0, 1, 2, 3, means i people out of 3 obtained the item selected.
XX follows binomial distribution with n = 3 & p : 0.7
Probability mass function of binomial distribution
P(X=x) = nCx *(p^x) * (1 – p)^(n–x)

here n= 3 ,p= 0.70 ,q= 0.30
XX = 0 means nobody got the item selected, so

Prob(XX = 0) = 3C0 · (0.7^0)· (0.3^3)

= 0.027

XX = 1 means only one person got the item selected, so

Prob(XX = 1) = 3C1 ·( 0.7)· (0.3^2)

= 0.189

XX = 2 means only two people got the item selected, so

Prob(XX = 2) = 3C2 · (0.7^2) ·(0.3)

= 0.441

XX = 3 means all three people got the item selected, so

Prob(XX = 3) = 3C3 ·( 0.7^3). (0.3^0)

= 0.343
3) ans
table :
XX Prob
0 0.027
1 0.189
2 0.441
3 0.343

2) ans
YY: number of markers selected which don't have ink.
YY = i where i = 0,1,2,3,4,5,6
means i markers do not have ink out of 7 selected markers .
All possible values of YY is 0,1,2,3,4,5,6