Solution:
First we will calculate Expected mean whcih can be calculated
as
Expected mean =
(Xi*(P(Xi)) = 0*0.1 + 1*0.15 + 2*0.2 + 3*0.55 = 0+0.15+0.4+1.65 =
2.2
X |
P(X) |
X*P(X) |
0 |
0.1 |
0 |
1 |
0.15 |
0.15 |
2 |
0.2 |
0.4 |
3 |
0.55 |
1.65 |
Standard deviation of Probability distribution cna be calculated
as
Standard deviation = sqrt(((Xi-mean)^2
*P(Xi)) = sqrt((0-2.2)^2*0.1 + (1-2.2)^2*0.15 + (2-2.2)^2*0.2 +
(3-2.2)^2*0.55)) = sqrt(0.484+0.216+0.008+0.352) = sqrt(1.06) =
1.03
X |
P(X) |
X*P(X) |
(Xi-mean) |
(Xi-mean)^2 |
(Xi-mean)^2*P(Xi) |
0 |
0.1 |
0 |
-2.2 |
4.84 |
0.484 |
1 |
0.15 |
0.15 |
-1.2 |
1.44 |
0.216 |
2 |
0.2 |
0.4 |
-0.2 |
0.04 |
0.008 |
3 |
0.55 |
1.65 |
0.8 |
0.64 |
0.352 |
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