Students in a college were classified according to years in school (X) and number of visits to a museum in the last year (Y = 0 for no visits, 1 for one visit, 2 for more than one visit). The joint probabilities in the accompanying table were estimated for these random variables. Number ofVisits (Y) Years in School (X) 1 2 3 4 0 1 2 0.07 0.13 0.04 0.05 0.11 0.04 0.03 0.17 0.09 0.02 0.15 0.10 a. Find the probability that a randomly chosen student has not visited a museum in the last year.b. Find the means of the random variables X and Y.c. Find and interpret the covariance between the random variables X and Y.
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.
Students in a college were classified according to years in school (X) and number of visits to a museum in the last year (Y = 0 for no visits, 1 for one visit, 2 for more than one visit). The joint probabilities in the accompanying table were estimated for these random variables.
| Number of Visits (Y) |
Years in School (X) | |||
| 1 | 2 | 3 | 4 | |
|
0 1 2 |
0.07 0.13 0.04 |
0.05 0.11 0.04 |
0.03 0.17 0.09 |
0.02 0.15 0.10 |
a. Find the probability that a randomly chosen student has not visited a museum in the last year.
b. Find the means of the random variables X and Y.
c. Find and interpret the
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