Question

You have your biased coin that lands heads 80% of the time. What is the expected value of a random variable defined as:

the number of heads in one biased coin flip (i.e. X=1 if heads and X=0 if tails)

Answer 1

The expected value for the number of heads in a single flip of a biased coin that lands heads 80% of the time is 0.80.

Step-by-step explanation:

The expected value of a random variable is a measure of the center of its distribution, calculated as the sum of all possible values each multiplied by the probability of occurrence. In the case of a biased coin flip where we denote the number of heads as X, and it is given that the coin lands as heads with a probability of 0.80 (or 80%), the expected value E(X) is calculated as follows:

• For X=1 (heads): P(X=1) = 0.80
• For X=0 (tails): P(X=0) = 0.20

The expected value E(X) is:

E(X) = (1 × P(X=1)) + (0 × P(X=0))
= (1 × 0.80) + (0 × 0.20)
= 0.80 + 0
= 0.80

Therefore, the expected value for the number of heads in one flip of a biased coin that lands heads 80% of the time is 0.80.