Question

Assignment 1 Wage Experience CollGrad 11 2 1 4 3 0 14 7 0 12 3 24 15 0 6 4 0 1
please explain all of 3 and 4 please

Answer 1

Wages	Experience	ColGrad
11	2	1
4	3	0
14	7	0
12	3	1
24	15	0
6	4	0

At the exchange rate 1 euro = 1.06125 dollars, we get the euro wages as -

Wages in dollar	Wages in Euro = dollar wage / 1.06125	Experience	ColGrad
11	10.365	2	1
4	3.769	3	0
14	13.192	7	0
12	11.307	3	1
24	22.615	15	0
6	5.654	4	0
	Total = 69.902

Mean = 69.902 / 6 = 11.15 euros

This is the mean wage.

Now for variance -

Wages in Euro = dollar wage / 1.06125	(x-mean)^2
10.365	0.6162
3.769	54.48
13.192	4.17
11.307	0.025
22.615	131.45
5.654	30.21
Total = 69.902	Total = 220.95

Variance = 220.95 / 5 = 44.19

Now -

To prove -

$COV(ax,by)=abCOV(x,y)$

We have. -

$COV(ax,by)=E[aX-E(aX)][bY-E(bY)]$

$\Rightarrow COV(ax,by)=E[aX-aE(X)][bY-bE(Y)]$

$\Rightarrow COV(ax,by)=aE[X-E(X)]b[Y-E(Y)]$

$\Rightarrow COV(ax,by)=(ab)E[X-E(X)][Y-E(Y)]$

$\Rightarrow COV(ax,by)=(ab)COV(x,y)$

Hence, proved.