In order to calculate the variance of a discrete probability distribution, all you need to do is follow the below simple steps and find the results manually with ease.
- Firstly, calculate each deviation from its mean or expected value.
- Now, square each value obtained in the first step.
- Next, product it by its probability and finally sum up the products.
- Thus, you can get the desired variance probability output.
- If you want to find the standard deviation(σ) of a probability distribution, simply calculate the square root of the variance(σ²).
Consider the rolling of a fair six-sided die, with X the number on the uppermost face. We know that the px of X is 16, x=1,2,3,4,5,6, and that mean is 3.5. What is the variance of random variable X?
px(X) = 16, μX = 3.5
To find the variance of random vaiable (X) of discrete probability function, use the formula of var(X) i.e.,
var(X) = E [(X−μX)^2]
= 35/12 ≈ 2.9167.
Therefore, the variance of probability distribution of X is approx 2.9167.
The standard deviation probability distribution of X is σX = √35/12 ≈ 1.7078.