An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table. y p(x, y) 0 5 10 15 x 0 0.01 0.06 0.02 0.10 5 0.04 0.14 0.20 0.10 10 0.01 0.15 0.16 0.01 (a) If the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score E(X + Y)? (Enter your answer to one decimal place.)(b) If the maximum of the two scores is recorded, what is the expected recorded score? (Enter your answer to two decimal places.)
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.
An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.
| y | |||||
|
p(x, y)
|
0 | 5 | 10 | 15 | |
| x | 0 | 0.01 | 0.06 | 0.02 | 0.10 |
| 5 | 0.04 | 0.14 | 0.20 | 0.10 | |
| 10 | 0.01 | 0.15 | 0.16 | 0.01 |
(b) If the maximum of the two scores is recorded, what is the expected recorded score? (Enter your answer to two decimal places.)
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