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If X represents the number of heads that appear when two coins are tossed, X_i={0,1,2}. Find the expected value of the random variable X.Select one:a.1b.2c.1d.4

Question

If X represents the number of heads that appear when two coins are tossed, X_i={0,1,2}. Find the expected value of the random variable X.Select one:a.1b.2c.1d.4

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Solution

To find the expected value of the random variable X, we need to calculate the weighted average of the possible outcomes.

Let's assign probabilities to each outcome:

  • X = 0 (no heads): P(X=0) = 1/4 (since there is only one way to get no heads: both coins landing on tails)
  • X = 1 (one head): P(X=1) = 2/4 (since there are two ways to get one head: HT or TH)
  • X = 2 (two heads): P(X=2) = 1/4 (since there is only one way to get two heads: both coins landing on heads)

Now, we can calculate the expected value using the formula: E(X) = Σ(X_i * P(X_i))

E(X) = (0 * 1/4) + (1 * 2/4) + (2 * 1/4) E(X) = 0 + 2/4 + 2/4 E(X) = 4/4 E(X) = 1

Therefore, the expected value of the random variable X is 1.

So, the correct answer is option c. 1.

This problem has been solved

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