Find the mean, variance and standard deviation of the probability distribution:
|
X |
2 |
3 |
4 |
|
P(X) |
0.2 |
0.5 |
0.3 |
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Mean = 3.1, Variance = 0.49, Standard deviation = 0.7
We construct the following table:
|
$x_i$ |
$p_i$ |
$p_ix_i$ |
$p_i{x_1}^2$ |
|
2 |
0.2 |
0.4 |
0.8 |
|
3 |
0.5 |
1.5 |
4.5 |
|
4 |
0.3 |
1.2 |
4.8 |
|
Total |
|
3.1 |
10.1 |
Mean = $μ = 3.1$
Variance = $Σp_i{x_i}^2- μ^2 = 10.1 - (3.1)^2 = 10.1-9.61 = 0.49$
Standard deviation = $\sqrt{0.49} = 0.7$