Question 3 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 Rand S are independent, what are the mean and standard deviation of the
distribution of R-S?
Mean 3 and standard deviation 1
B
Mean 3 and standard deviation 5
Mean 3 and standard deviation 7
mong
D
Mean 17 and standard deviation 1
E
Mean 17 and standard deviation 5

(B) Mean 3 and standard deviation 5

Step-by-step explanation:

Property of mean

The mean of the sum or difference of two random variable R and S is the sum of their means.

μ (R-S) = μ(R) - μ(S)

μ(R-S) = 10 - 7 = 3

Property of standard deviation

The variance of Independent variable R and S is is the sum of their variances. Even when we subtract two random variables, we still add their variances; subtracting two variables increases the overall variability in the outcomes.

σ^2(R-S) = σ^2 (R) + σ^2(S)

            = 16 + 9           ( variance = (standard deviation)^2  )

             = 25

σ(R-S)  = 5