The standard deviation of the distribution is 1.92
How to determine the standard deviation of the distribution
From the question, we have the following parameters that can be used in our computation:
The table of values
Where, we have
x P(x)
0 0.1
1 0.2
2 0.1
3 0.6
Start by calculating the expected value using
E(x) = Sum of x * P(x)
So, we have
E(x) = 0 * 0.1 + 1 * 0.2 + 2 * 0.1 + 3 * 0.6
E(x) = 2.2
Next, we have
E(x²) = 0 * 0.1² + 1 * 0.2² + 2 * 0.1² + 3 * 0.6²
E(x²) = 1.14
So, we have
Var(x) = [E(x)]² - E(x²)
This gives
Var(x) = (2.2)² - (1.14)
Var(x) = 3.7
Lastly, we have
SD(x) = √3.7
SD(x) = 1.92
Hence, the standard deviation of the distribution is 1.92