A random variable X takes the values 1, 2 and 3 with \(P(X = 1) = a\), \(P(X = 2) = b\) and \(P(X = 3) = 0.3\). If \(E(X) = 2.1\), then
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(a = 0.2,\ b = 0.5\)
The probabilities add up to 1:
\(a + b + 0.3 = 1\)
\(a + b = 0.7\)
The mean is given:
\(1(a) + 2(b) + 3(0.3) = 2.1\)
\(a + 2b = 1.2\)
Subtracting the first equation from the second:
\(b = 0.5\)
\(a = 0.7 - 0.5 = 0.2\)