The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S has mean 7 and standard deviation 3. If R and S are independent, what are the mean and standard deviation of the distribution of R−S ?

A) Mean 3 and standard deviation 1

B) Mean 3 and standard deviation 5

C) Mean 3 and standard deviation 7

D) Mean 17 and standard deviation 1

E) Mean 17 and standard deviation 5

B

Mean of 3 and Standard deviation of 5

Explanation:

Performing operations on means of independent variables is similar to performing arithmetic operations on natural numbers.

Subtracting the mean of S from R is 10 - 7 = 3

For the difference in standard deviation. It should be noted that when combining variables, the variation within the distribution. So therefore, adding or subtraction of variables, the variation will increase and will yield same answer.

To obtain the difference in standard deviation, the variances of the random variables has to be added and then the square root will be taken to return back to standard deviation.

SD(R-S)=sqrt(R²+S²)

SD=sqrt(4²+3³)

SD=sqrt(25)

SD=5