If the probability distribution table for no, of "Heads'' in three throws of coin is
|
X |
0 |
1 |
2 |
3 |
|
P(X=x) |
1/8 |
3/8 |
3/8 |
1/8 |
Then Var (X) is:
Answer & explanation
Correct answer: option 1
|
xi |
Pi |
Pixi |
Pixi2 |
|
0 |
1/8 |
0 |
0 |
|
1 |
3/8 |
3/8 |
3/8 |
|
2 |
3/8 |
6/8 |
12/8 |
|
3 |
1/8 |
3/8 |
9/8 |
|
|
|
$∑Pixi=\frac{12}{8}=\frac{3}{2}$ |
$∑Pixi^2=\frac{24}{8}=3$ |
$Var(X)=∑P_ix_i^2-(∑P_ix_i)^2 = 3-(\frac {3}{2})^2=\frac{3}{1}-\frac {9}{4}=\frac {12-9}{4}=\frac{3}{4}$