A random variable X with probability distribution is given below X = x_i 2 3 4 5 P(X = x_i) 5 k 7 k 9 k 11 k

Step-by-step solution

For a probability distribution, the sum of all probabilities must be equal to 1. P(X=x_i) = 5 k + 7 k + 9 k + 11 k = 1 5+7+9+11 k = 1 32 k = 1 k = 32 The mean of the distribution is given by E(X) = x_i P(X=x_i) . E(X) = 2 5 32 + 3 7 32 + 4 9 32 + 5 11 32 E(X) = 10 32 + 21 32 + 36 32 + 55 32 E(X) = 10 + 21 + 36 + 55 32 = 122 32 Simplifying the fraction by dividing numerator and denominator by 2: E(X) = 61 16 Answer: 61 16