If i have a binomial distribution with number of trials 20 and success rate 0.2 how do i calculate expected value and variance, I am new to statistics and a detailed answer or explanation will be appreciated. Thanks in advance
2026-03-28 12:38:25.1774701505
binomial distribution probability for expected value and variance
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Expected Value is what it sounds like: what's the expected value after many trials? For here, if we have 20 trials with a success rate of $20%$, then $20 \cdot 20\%$ is the Expected Value since all $20$ have the same success rate.
Variance, simplified, is the average of the squared differences from the Mean. Let's say you have two numbers, $10$ and $15$ and you want to find the variance. First, you find the mean, which is obviously $12.5$. Then, you must calculate the difference from the mean. $12.5-10 = 2.5$ and $15-12.5 = 2.5$. You then square these values, so in this case you get $2.5^2+2.5^2 = 12.5$. Finally, you divide by the number of terms just like the mean. Variance is now $6.25$.
-FruDe