Respuesta :
Answer:
S = I-E.
We can find the expected value of S and we got:
[tex] E(S) = E(I-E) = E(I) -E(E)= 682-211=471[/tex]
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:
[tex] Var(S) = Var(I-E) = Var(I) +Var(E) - 2Cov(I,E)[/tex]
And since we know that [tex] Cov (I,E) =0[/tex] then we have:
[tex] Var(S) = Var(I) + Var(E) = 49^2 + 16^2 = 2657[/tex]
And then the deviation would be:
[tex] Sd(S) = \sqrt{2657}= 51.546[/tex]
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:
[tex] E(I) = 682, \sigma_I = 49[/tex]
Let E the random variable that represent the monthly expenses for each month and we know:
[tex] E(E)= 211, \sigma_E = 16[/tex]
And for this case we know that the random variables I and E are independent, so then [tex] Cov(I, E) = 0[/tex]
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:
[tex] E(S) = E(I-E) = E(I) -E(E)= 682-211=471[/tex]
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:
[tex] Var(S) = Var(I-E) = Var(I) +Var(E) - 2Cov(I,E)[/tex]
And since we know that [tex] Cov (I,E) =0[/tex] then we have:
[tex] Var(S) = Var(I) + Var(E) = 49^2 + 16^2 = 2657[/tex]
And then the deviation would be:
[tex] Sd(S) = \sqrt{2657}= 51.546[/tex]
And that represent the standard deviation of the amount of money you put in your savings account each month
