Question

Let X is denoted as the number of heads in three tosses of a coin. Determine the mean and variance for the random variable X.

(a) 4.8

(b) 6

(c) 3.2

(d) 1.5

I got this question during an interview.

Asked question is from Discrete Probability topic in division Discrete Probability of Discrete Mathematics

Answer 1

Right choice is (d) 1.5

The best explanation: Let H represents a head and T be a tail. X denotes the number of heads in three tosses of a coin. X can take the value 0, 1, 2, 3. P(X = 0) = \(\frac{1}{8}\), P(X = 1) = \(\frac{3}{8}\), P(X = 2) = \(\frac{3}{8}\), P(X = 3) = \(\frac{1}{8}\). The probability distribution of X is E(X) = Σixipi = 1 × \(\frac{3}{8} + 2 × \frac{3}{8} + 3 × \frac{1}{8}\) = 1.5. E(X2) = \(12 × \frac{3}{8} + 22 × \frac{3}{8} + 32 × \frac{1}{8}\) = 3. So, Variance of X = V(X) = E(X^2) – [E(X)]^2 = 3 – 1.5 = 1.5.