The accompanying table shows, for credit-card holders with one to three cards, the joint probabilities for number of cards owned (X) and number of credit purchases made in a week (Y). Number ofCards (X) Number of Purchases in Week (Y) 0 1 2 3 4 1 2 3 0.08 0.03 0.01 0.13 0.08 0.03 0.09 0.08 0.06 0.06 0.09 0.08 0.03 0.07 0.08 a. For a randomly chosen person from this group, what is the probability distribution for number of purchases made in a week?b. For a person in this group who has three cards, what is the probability distribution for number of purchases made in a week?c. Are number of cards owned and number of purchases made statistically independent?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The accompanying table shows, for credit-card holders with one to three cards, the joint probabilities for number of cards owned (X) and number of credit purchases made in a week (Y).
| Number of Cards (X) |
Number of Purchases in Week (Y) | ||||
| 0 | 1 | 2 | 3 | 4 | |
|
1 2 3 |
0.08 0.03 0.01 |
0.13 0.08 0.03 |
0.09 0.08 0.06 |
0.06 0.09 0.08 |
0.03 0.07 0.08 |
a. For a randomly chosen person from this group, what is the
b. For a person in this group who has three cards, what is the probability distribution for number of purchases made in a week?
c. Are number of cards owned and number of purchases made statistically independent?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
