Question

4. In the 2 data sets below find the expected value and variance. Then promise to think about while the mean is the same why variance is different in the 2

x	P(x)
1	0.1
2	0.3
3	0.45
4	0.15

y	P(y)
-1000	0.38675
-100	0.1
100	0.1265
1000	0.38675

Answer 1

2 Х P(x) 0.10 X P(x) 0.10 0.60 1 1 x2 P(x) 0.10 1.20 4.05 2 0.30 4 0.45 1.35 9 4 0:15 0.60 16 2.40 x. P(x) Expected value Elx) = mean 0.10+ 0.60+ 1.35 to 60 2.65 E (x2) = Š x2 P(x) = 0.10+ 1.20 + 4.05 +2.40 7.75 2 E(+2) -[E(x)] 2 Variance (x) = v(x) = 7.75 (2.65) li 10.7275 y2 Y У - 1000 P(Y) 0.38675 Y P(Y) - 386.75 y² ply) 386750 106 104 1000 -100 100 0:10 0:1265 0.38675 10. 12.65 386.75 104 1265 1000 106 386750 Ely) E Y PO = - 386.75 -10 + 12.65 + 386.75 2.65 1265 + 386750 Ely2) = { y² Ply) = 386750 + 1000 t 7 75 765 Variance (Y) E(Y2) - [[(y)] ² 775 765 (2.652 7 75 757.97

с are Mean is same because the weighted overage is same for both the distribution Variance for for data set 1 is small because the observations centered around while variance for data set 2 is large because the observations very far away away from the meano - mean, are