11.2 Problems on mathematical expectation  (Page 3/6)

(See Exercise 4 from "Problems On Random Vectors and Joint Distributions", m-file npr08_04.m ). As a variation of [link] , suppose a pair of dice is rolled instead of a single die. Determine the joint distribution for $\{X,Y\}$ and determine $E\left[Y\right]$ .

(See Exercise 5 from "Problems On Random Vectors and Joint Distributions", m-file npr08_05.m ). Suppose a pair of dice is rolled. Let X be the total number of spots which turn up. Roll the pair an additional X times. Let Y be the number of sevens that are thrown on the X rolls. Determine the joint distribution for $\{X,Y\}$ and determine $E\left[Y\right]$ .

(See Exercise 6 from "Problems On Random Vectors and Joint Distributions", m-file npr08_06.m ). The pair $\{X,Y\}$ has the joint distribution:

Determine $E\left[X\right]$ , $E\left[Y\right]$ , $E\left[X^2\right]$ , $E\left[Y^2\right]$ , and $E\left[XY\right]$ .

(See Exercise 7 from "Problems On Random Vectors and Joint Distributions", m-file npr08_07.m ). The pair $\{X,Y\}$ has the joint distribution:

Determine $E\left[X\right]$ , $E\left[Y\right]$ , $E\left[X^2\right]$ , $E\left[Y^2\right]$ , and $E\left[XY\right]$ .

(See Exercise 8 from "Problems On Random Vectors and Joint Distributions", m-file npr08_08.m ). The pair $\{X,Y\}$ has the joint distribution:

Determine $E\left[X\right]$ , $E\left[Y\right]$ , $E\left[X^2\right]$ , $E\left[Y^2\right]$ , and $E\left[XY\right]$ .

(See Exercise 9 from "Problems On Random Vectors and Joint Distributions", m-file npr08_09.m ). Data were kept on the effect of training time on the time to performa job on a production line. X is the amount of training, in hours, and Y is the time to perform the task, in minutes. The data are as follows:

Determine $E\left[X\right]$ , $E\left[Y\right]$ , $E\left[X^2\right]$ , $E\left[Y^2\right]$ , and $E\left[XY\right]$ .