Question

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 )?

Explanation:

Step1: Calculate mean of $R-S$

$\mu_{R-S} = \mu_R - \mu_S = 10 - 7 = 3$

Step2: Calculate variance of $R-S$

$\sigma^2_{R-S} = \sigma^2_R + \sigma^2_S = 4^2 + 3^2 = 16 + 9 = 25$

Step3: Calculate standard deviation of $R-S$

$\sigma_{R-S} = \sqrt{\sigma^2_{R-S}} = \sqrt{25} = 5$

Answer:

Mean: $3$, Standard deviation: $5$