Two random variables x and y are independent if the value of x does not affect t

Question

Two random variables x and y are independent if the value of x does not affect the value of y. If the variables are not independent, they are dependent. A new random variable can be formed by finding the sum or difference of random variables. If a random variable x has mean mu Subscript x and a random variable y has mean

mu Subscript y then the means of the sum and difference of the variables are given by the following equations.

mu Subscript x plus y Baseline equals mu Subscript x Baseline plus mu Subscript y

nbsp mu Subscript x minus y Baseline equals mu Subscript x Baseline minus mu Subscript y

The distribution of a test's scores for college-bound male seniors has a mean of 1524 and a standard deviation of 319

The distribution of a test's scores for college-bound female seniors has a mean of 1492 and a standard deviation of 305. One male and one female are randomly selected. Assume their scores are independent.

What is the average sum of their scores? What is the average difference of their scores?

A) What is the average sum of their scores?

(Type an integer or a decimal.)

B) What is the average difference of their scores?

(Type an integer or a decimal.)

mu Subscript x plus y Baseline equals mu Subscript x Baseline plus mu Subscript y

Explanation / Answer

A)

Average sum of their score= mu_x + mu_y = 1524+ 1492=

=3016

Ans=3016

B)

average difference of their score= mu_x-mu_y = 1524- 1492

=32

Ans=32

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