Suppose you are conducting an experiment by tossing two coins simultaneously. You define a random variable X as the number of tails you get in each trial of the experiment. What is the expected value of X?

To find the expected value of X, we need to determine the probability of each possible outcome and multiply it by the corresponding value of X.

In this experiment, there are four possible outcomes when tossing two coins simultaneously:

1. Both coins land on heads (HH)
2. One coin lands on heads and the other on tails (HT or TH)
3. Both coins land on tails (TT)

Let's calculate the probability of each outcome:

1. Probability of HH: Since each coin has a 50% chance of landing on heads, the probability of both coins landing on heads is (0.5) * (0.5) = 0.25.

2. Probability of HT or TH: There are two possible ways to get one head and one tail, so the probability is 2 * (0.5) * (0.5) = 0.5.

3. Probability of TT: Similar to the first outcome, the probability of both coins landing on tails is (0.5) * (0.5) = 0.25.

Now, let's assign the value of X to each outcome:

• HH: X = 0 tails
• HT or TH: X = 1 tail
• TT: X = 2 tails

To find the expected value, we multiply each outcome's probability by its corresponding value of X and sum them up:

Expected value of X = (0 * 0.25) + (1 * 0.5) + (2 * 0.25) = 0 + 0.5 + 0.5 = 1.

Therefore, the expected value of X in this experiment is 1.