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Your friend Albert has invented a game involving two ten-sided dice. One of the dice has threes, fours, and fives on its faces, the other has sixes, eights, and tens. He won’t tell you how many of each number there are on the faces, but he does tell you that if X = the result of a single roll of the first die and Y = the result of a single roll of the second die, then [tex]\mu_x[/tex] =3.6, [tex]\sigma_x[/tex] =0.8, [tex]\mu_y[/tex] =8.0 and [tex]\sigma_y[/tex] =0.9. Let Z = the sum of the two dice when each is rolled once.
What is the expected value of Z?
a. 1.7
b. 4.4
c. 5.8
d. 11.6

Respuesta :

Answer:

d. 11.6

Step-by-step explanation:

The results of the first die and the second one are independent to each other. The expected value of Z is obtained, therefore, by summing the expected values of both X and Y, because Z = X+Y and X and Y are independent. As a result [tex] \mu_z = \mu_x + \mu_y = 3.6+8.0 = 11.6 . [/tex]