Question

You work at a job where your average monthly earnings are $682 with a standard deviation of $49. Your mean monthly expenses are S211 with a standard deviation of $16. Assume that the your monthly earnings and expenses are independent. You put any extra money that you have at the end of the month into your savings account. What is the mean of the amount of money you put in your savings account each month? Preview What is the standard deviation of the amount of money you put in your savings account each month?

Answer 1

Answer:

S = I-E.

We can find the expected value of S and we got:

$E(S) = E(I-E) = E(I) -E(E)= 682-211=471$

And that represent the mean of the amount of money into your savings account each month

And now we can find the variance of the random variable S like this:

$Var(S) = Var(I-E) = Var(I) +Var(E) - 2Cov(I,E)$

And since we know that $Cov (I,E) =0$ then we have:

$Var(S) = Var(I) + Var(E) = 49^2 + 16^2 = 2657$

And then the deviation would be:

$Sd(S) = \sqrt{2657}= 51.546$

And that represent the standard deviation of the amount of money you put in your savings account each month

Step-by-step explanation:

Let I the random variable that represent the income for each month and we know:

$E(I) = 682, \sigma_I = 49$

Let E the random variable that represent the monthly expenses for each month and we know:

$E(E)= 211, \sigma_E = 16$

And for this case we know that the random variables I and E are independent, so then $Cov(I, E) = 0$

We can define the random variable S representing the amount that we can save each month and we can define S = I-E.

We can find the expected value of S and we got:

$E(S) = E(I-E) = E(I) -E(E)= 682-211=471$

And that represent the mean of the amount of money into your savings account each month

And now we can find the variance of the random variable S like this:

$Var(S) = Var(I-E) = Var(I) +Var(E) - 2Cov(I,E)$

And since we know that $Cov (I,E) =0$ then we have:

$Var(S) = Var(I) + Var(E) = 49^2 + 16^2 = 2657$

And then the deviation would be:

$Sd(S) = \sqrt{2657}= 51.546$

And that represent the standard deviation of the amount of money you put in your savings account each month