The binomial distribution is used to calculate probabilities when a trial with two outcomes is repeated a certain number of times. For example, suppose that a coin is tossed ten times. Then the probability that we get heads 6 times can be calculated using the binomial distribution.
We can also calculate the expected value for the number of times we get heads using the expected value formula for the binomial distribution. Let X be a random variable following the binomial distribution with parameters ‘n’ and ‘p’. Then the expected value of X can be calculated using the formula,
Expected Value E(X) = n*p
Here, n denotes the total number of trials and p denotes the probability of success.
Let us try to understand the above formula by an example.
Example:
Suppose that a coin is tossed 15 times. Calculate the expected number of heads obtained.
Solution: The outcome’s heads and tails are labeled as success and failure respectively. Here, we have n=15 since the coin is tossed 15 times. Also, the probability of getting heads (success) is p=0.5.
Hence, Expected Value E(X) = n*p = 15*0.5 = 7.5
So one expects to get heads an average of 7.5 times when a coin is tossed 15 times.
Expected Value Calculator:
The below calculator calculates the expected value for a binomial random variable. Given the probability of success (p) and the number of trials (n), the calculator provides the expected value of the random variable.
Expected Value E(x):
