A random variable X has the following probability distributions
| $X=x_i:$ | 1 | 2 | 3 | 4 |
| $P(X=x_i):$ | 0.1 | 0.2 | 0.3 | 0.4 |
The mean and standard deviation of X are respectively.
Answer & explanation
Correct answer: option 2
The computation of mean and standard deviation is as follows:
| $x_i$ | $p_i=P(X=x_i)$ | $p_ix_i$ | $p_ix_i^2$ |
|
1 2 3 4 |
0.1 0.2 0.3 0.4 |
0.1 0.4 0.9 1.6 |
0.1 0.8 2.7 6.4 |
| $∑p_ix_i=3$ | $∑p_ix_i^2=10$ |
$∴Mean = ∑p_ix_i=3$
Variance (X)= $∑p_ix_i^2-(∑p_ix_i)^2=10-9=1$