Respuesta :
Answer:
(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
The mean of the distribution of R-S is 3 and the standard deviation of the distribution of R-S is 5 and this can be determined by using the given data.
Given :
- The distribution of random variable R has a mean of 10 and a standard deviation of 4.
- The distribution of random variable S has mean 7 and standard deviation 3.
The following steps can be used in order to determine the mean and standard deviation of the distribution of R-S:
Step 1 - The mean can be determined by using the below formula.
[tex]\rm \mu(R-S) = \mu(R)-\mu(S)[/tex]
Step 2 - Substitute the values of [tex]\rm \mu(R)[/tex] and [tex]\rm \mu(S)[/tex] in the above expression.
[tex]\rm \mu(R-S) = 10-7[/tex]
[tex]\rm \mu(R-S) = 3[/tex]
Step 3 - The standard deviation can be determined by using the below formula.
[tex]\rm \sigma^2(R-S) = \sigma^2(R)+\sigma^2(S)[/tex]
Step 4 - Substitute the values of [tex]\rm \sigma(R)[/tex] and [tex]\rm \sigma(S)[/tex] in the above expression.
[tex]\rm \sigma^2(R-S) = 16+9[/tex]
[tex]\rm \sigma(R-S) = 5[/tex]
Therefore, the correct option is B).
For more information, refer to the link given below:
https://brainly.com/question/12402189
