In a binomial experiment, the probability of success in each trial is 0.2 and 40 trials are performed. Let 𝑋 be the random variable, which counts the number of successes. Find the variance of 𝑋.
Let’s firstly look at the two key properties of a binomial experiment. Firstly, it consists of 𝑛 repeated independent trials. There are only two possible outcomes from each trial: success and failure. A binomial experiment has two key values denoted by 𝑛 and 𝑝. 𝑛 is the number of trials and 𝑝 is the probability of success.
In this particular question, the value of 𝑛 is 40 and the value of 𝑝 is 0.2. When dealing with a binomial experiment, the mean denoted by 𝐸 of 𝑋, the expected value, is equal to 𝑛 multiplied by 𝑝. The variance, or Var of 𝑋, is equal to 𝑛 multiplied by 𝑝 multiplied by one minus 𝑝. In this question, the variance is equal to 40 multiplied by 0.2 multiplied by 0.8. This is equal to 6.4.
A binomial experiment with 40 trials and probability of success of 0.2 has a variance of 6.4.