Probability
Random variable distribution
nta_pyq_2025_apr
Grade 12
Question:
Let a random variable X take values 0, 1, 2, 3 with$P(X = 0) = P(X = 1) = p$,$P(X = 2) = P(X = 3)$and 2 E (X$) = 2E(X)$. Then the value of$8p - 1$is :
Step-by-Step Solution
Key Concept: Compute the favourable cases for random variable distribution and divide by the total equally likely cases.
$2p + 2q = 1$2 (2)$p + q$3 2 2 E (x ) =$\sum$x p (xi$) = 0$$\cdot$$p + 1$$\cdot$$p + 4$$\cdot$$q + 9q$i$i=0 = p + 13q$3 2 E(x) =$\sum$x p (xi$) = 0$$\cdot$$p + 1$$\cdot$$p + 2q + 3q = p + 5q$i$i=0$$p + 13q = 2(p + 5q)$$p = 3q$1 3 So, q = &$p = 8$8 So,$8p - 1 = 2$Option (2)
Correct Answer: 2