A real estate agent is interested in the relationship between the number of lines in a newspaper advertisement for an apartment and the volume of inquiries from potential renters. Let volume of inquiries be denoted by the random variable X, with the value 0 for little interest, 1 for moderate interest, and 2 for strong interest. The real estate agent used historical records to compute the joint probability distribution shown in the accompanying table. Numberof Lines (Y) Number of Inquiries (X) 0 1 2 3 4 5 0.09 0.07 0.03 0.14 0.23 0.10 0.07 0.16 0.11 a. Find the joint cumulative probability at X = 1, Y = 4, and interpret your result.b. Find and interpret the conditional probability distribution for Y, given X = 0.c. Find and interpret the conditional probability distribution for X, given Y = 4.d. Find and interpret the covariance between X and Y.e. Are number of lines in the advertisement and volume of inquiries independent of one another?
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.
A real estate agent is interested in the relationship between the number of lines in a newspaper advertisement for an apartment and the volume of inquiries from potential renters. Let volume of inquiries be denoted by the random variable X, with the value 0 for little interest, 1 for moderate interest, and 2 for strong interest. The real estate agent used historical records to compute the joint
| Number of Lines (Y) |
Number of Inquiries (X) | ||
| 0 | 1 | 2 | |
|
3 4 5 |
0.09 0.07 0.03 |
0.14 0.23 0.10 |
0.07 0.16 0.11 |
a. Find the joint cumulative probability at X = 1, Y = 4, and interpret your result.
b. Find and interpret the conditional probability distribution for Y, given X = 0.
c. Find and interpret the conditional probability distribution for X, given Y = 4.
d. Find and interpret the
e. Are number of lines in the advertisement and volume of inquiries independent of one another?
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