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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) 1.5I got this question during an interview.Asked question is from Discrete Probability topic in division Discrete Probability of Discrete Mathematics

Answer»

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.


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