The probability distribution of a discrete random variable X is ( array ||c|c|c|c|c|c| X & 0 & 1 & 2 & 3 & 4 P ( X =x) & 2 k & k & 2 k & 4 k & k array ) If a = P (x < 3) and b = P (2 < x < 4) , then

Step-by-step solution

A discrete random variable X has the probability distribution: X 0 1 2 3 4 P(X=x) 2k k 2k 4k k Since the sum of all probabilities must equal 1 , we have 2k + k + 2k + 4k + k = 10k = 1 , so k = 1 10 . The value a is defined as P(X The value b is P(2 Comparing a = 1 2 and b = 2 5 , we see that 1 2 = 0.5 > 0.4 = 2 5 , so a > b . Final answer: B