Find the mean number of heads in three tosses of a fair coin.

Solution:

Three times, a coin is tossed.

Three coins are flung at the same time. As a result, the experiment’s sample space is \{HHH, HHT, HTH, THH, TTH, THT, HTT, TTT\}. The number of heads is represented by .

As we can see, is a sample space function with a range of .

As a result, is a random variable with values of , or 3.

As a result, the necessary probability distribution is,

Therefore mean is:

We may now retrieve the result by swapping the values.