The roll of a pair of dice has the following probability distribution,where the random variable is the sum of the values produced by each die: Calculate the expected value of x.
A)6
B)7
C)8

Question

The roll of a pair of dice has the following probability distribution,where the random variable is the sum of the values produced by each die:  Calculate the expected value of x.
A)6 
B)7 
C)8

Quizplus · Accepted Answer

To calculate the expected value of x, we need to multiply each possible outcome by its probability and then add all the products together. From the probability distribution given, we can write:

E(x) = (1/36)×2 + (2/36)×3 + (3/36)×4 + (4/36)×5 + (5/36)×6 + (6/36)×7 + (5/36)×8 + (4/36)×9 + (3/36)×10 + (2/36)×11 + (1/36)×12

Simplifying this expression, we get:

E(x) = (1/36)(2+12) + (2/36)(3+11) + (3/36)(4+10) + (4/36)(5+9) + (5/36)(6+8) + (6/36)×7

E(x) = (1/36)×14 + (2/36)×14 + (3/36)×14 + (4/36)×14 + (5/36)×14 + (6/36)×7

E(x) = (14/36)×(1+2+3+4+5) + (6/36)×7

E(x) = (14/36)×15 + (6/36)×7

E(x) = 5.833 + 1.167

E(x) = 7

Therefore, the expected value of x is 7, and the best choice is B.

The Roll of a Pair of Dice Has the Following