A researcher suspected that the number of betweenmeal snacks eaten by students in a day during final examinations might depend on the number of tests a student had to take on that day. The accompanying table shows joint probabilities, estimated from a survey. Number ofSnacks (Y) Number of Tests (X) 0 1 2 3 0 1 2 3 0.07 0.07 0.06 0.02 0.09 0.06 0.07 0.04 0.06 0.07 0.14 0.16 0.01 0.01 0.03 0.04 a. Find the probability distribution of X and compute the mean number of tests taken by students on that day.b. Find the probability distribution of Y and, hence, the mean number of snacks eaten by students on that day.c. Find and interpret the conditional probability distribution of Y, given that X = 3.d. Find the covariance between X and Y.e. Are number of snacks and number of tests independent of each other?
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 researcher suspected that the number of betweenmeal snacks eaten by students in a day during final examinations might depend on the number of tests a student had to take on that day. The accompanying table shows joint probabilities, estimated from a survey.
| Number of Snacks (Y) |
Number of Tests (X) | |||
| 0 | 1 | 2 | 3 | |
|
0 1 2 3 |
0.07 0.07 0.06 0.02 |
0.09 0.06 0.07 0.04 |
0.06 0.07 0.14 0.16 |
0.01 0.01 0.03 0.04 |
a. Find the probability distribution of X and compute the
b. Find the probability distribution of Y and, hence, the mean number of snacks eaten by students on that day.
c. Find and interpret the conditional probability distribution of Y, given that X = 3.
d. Find the
e. Are number of snacks and number of tests independent of each other?
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