1 Answer

PiyushRathi · Answer 1 · 2021-08-21T21:08:34+0000

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) = √(2657)= 51.546

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

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.