Statistics And Probability Question 331
Question: The variance of the following distribution is
| $x_{i}$ | 2 | 3 | 11 |
|---|---|---|---|
| $f(x_{i})$ | $ \frac{1}{3} $ | $ \frac{1}{2} $ | $ \frac{1}{6} $ |
Options:
A) 10
B) 16
C) 8
D) 7.5
Show Answer
Answer:
Correct Answer: A
Solution:
[a] We construct the following table:
| $x_{i}$ | $f(x_{i})$ | $x_i^{2}$ | $f(x_{i}).x_{i}$ | $f(x_{i}).x_{_{i}}^{2}$ |
|---|---|---|---|---|
| 2 | $\frac{1}{3}$ | 4 | $\frac{2}{3}$ | $\frac{4}{3}$ |
| 3 | $\frac{1}{2}$ | 9 | $\frac{3}{2}$ | $\frac{9}{2}$ |
| 11 | $\frac{1}{6}$ | 121 | $\frac{11}{6}$ | $\frac{121}{6}$ |
| 1 | 4 | 26 |
$ \therefore $ Variance $ {{\sigma }^{2}}=\frac{\sum{f(x_{i}).x_i^{2}}}{\sum{f(x_{i})}}-{{( \frac{\sum{f(x_{i})x_{i}}}{\sum{f(x_{i})}} )}^{2}} $ $ =\frac{26}{1}-{{( \frac{4}{1} )}^{2}}=26-16=10 $
BETA
