The expressions of red die, and green die are illustrations of expected values
We have the following parameters from the complete question
[tex]E(X) = \frac 72[/tex]
[tex]E(Y) = \frac 72[/tex]
(a) Calculate E(X + Y)
Since X and Y are independent random variables, then
[tex]E(X + Y) = E(X) + E(Y)[/tex]
So, we have:
[tex]E(X + Y) = \frac 72 + \frac 72[/tex]
Take LCM
[tex]E(X + Y) = \frac{7+ 7}2[/tex]
Add 7 and 7
[tex]E(X + Y) = \frac{14}2[/tex]
Divide 14 by 2
[tex]E(X + Y) = 7[/tex]
Hence, the value of E(X + Y) is 7/2
(b) Calculate E(X - Y)
Since X and Y are independent random variables, then
[tex]E(X - Y) = E(X) - E(Y)[/tex]
So, we have:
[tex]E(X - Y) = \frac 72 - \frac 72[/tex]
Take LCM
[tex]E(X - Y) = \frac{7- 7}2[/tex]
Subtract 7 from 7
[tex]E(X - Y) = \frac{0}2[/tex]
Divide 0 by 2
[tex]E(X + Y) = 0[/tex]
(b) Calculate E(X - Y)
Since X and Y are independent random variables, then
[tex]E(X - Y) = E(X) - E(Y)[/tex]
So, we have:
[tex]E(X - Y) = \frac 72 - \frac 72[/tex]
Take LCM
[tex]E(X - Y) = \frac{7- 7}2[/tex]
Subtract 7 from 7
[tex]E(X - Y) = \frac{0}2[/tex]
Divide 0 by 2
[tex]E(X - Y) = 0[/tex]
Hence, the value of E(X - Y) is 0
(c) Calculate E(XY)
Since X and Y are independent random variables, then
[tex]E(X Y) = E(X) \times E(Y)[/tex]
So, we have:
[tex]E(XY) = \frac 72 \times \frac 72[/tex]
Multiply
[tex]E(XY) = \frac{49}4[/tex]
Hence, the value of E(XY) is 0
Read more about expected values at:
https://brainly.com/question/13005177
