Chapter 6.2, Problem 55E

(a)

To determine

To find: that calculation of the mean of the total rainfall X +Y to be ${\mu }_X+{\mu }_y$

Answer to Problem 55E

Yes

Explanation of Solution

Yes, it is reasonable the reason is that the following property of the mean is having for all possible pairs of variables

  ${\mu }_{X+Y}={\mu }_X+{\mu }_y$

And therefore the mean of X +Y is ALWAYS equal to ${\mu }_X+{\mu }_y$ .

(b)

To determine

To find: that calculation of the variation of the total rainfall to be ${\sigma }_X^2+{\sigma }_Y^2$

Answer to Problem 55E

No, independence is required.

Explanation of Solution

No, it is not reasonable the reason is that the property of the variance only holds when the variables X and Y are independent.

  ${\sigma }_{X+Y}^2={\sigma }_X^2+{\sigma }_Y^2$