Suppose you have a coin that lands on Heads with probability 0.6

There are three coin flips defined as X. Heads count 1 and tails count 0 – e.g., if three heads then X= 3; if a
head and two tails then X = 1; if three tails the X = 0.

What is the expected value of X?

I'm confused as to how to start this problem?

To find the expected value of X, you need to calculate the weighted average of all possible outcomes. In this case, the outcomes are the different values of X, which can be 0, 1, 2, or 3.

To get started, we'll calculate the probability of each outcome occurring. Since the coin lands on heads with a probability of 0.6, the probability of tails is 1 - 0.6 = 0.4. We can use this information to calculate the probabilities for each outcome.

- The probability of X = 0 (three tails) is (0.4) * (0.4) * (0.4) = 0.064 (since each flip is independent, we multiply the probabilities).
- The probability of X = 1 (two tails and one head) is (0.4) * (0.4) * (0.6) = 0.096.
- The probability of X = 2 (one tail and two heads) is (0.4) * (0.6) * (0.6) = 0.144.
- The probability of X = 3 (three heads) is (0.6) * (0.6) * (0.6) = 0.216.

Now that we have the probabilities, we can calculate the expected value by multiplying each outcome by its probability and summing them up:

Expected value of X = (0 * 0.064) + (1 * 0.096) + (2 * 0.144) + (3 * 0.216)

Simplifying this expression will give you the solution for the expected value of X.