Question

Question: What is the variance of the number of heads that come up when a fair coin is flipped 10 times?

Short answer

Answer:So, the expected value of the random variable is: 2.5

Step-by-step solution

Given data

A fair coin is flipped \(10\)times.

Definition

The term variance refers to a statistical measurement of the spread between numbers in a data set. The variance measures how far each number in the set is from the mean and thus from every other numbers in the set.

Calculation

Here, flipping a coin is a Bernoulli trial with\(n = 10\)with success as getting a head with probability\(p = 1/2\).

So, we need to find the variance of the number of success in\(n\)Bernoulli trials.

The variance of the number of success in \(n\)Bernoulli trials is \(np(1 - p)\)

Final step 

Hence, the variance is \(\begin{array}{l}np(1 - p) = 10.(1/2).(1 - 1/2)\\np(1 - p) = 10.(1/2).(1/2)\\np(1 - p) = 2.5\end{array}\)

So, the expected value of random number is \(2.5\).