COMEDK2023Evening ShiftMathematicsProbabilityActual
The probability distribution of a discrete random variable X is given as X 1 2 4 2A 3A 5A P(X) 1 2 1 5 3 25 K 1 25 1 25 Then the value of A if E(X)=2.94 is
Options
- A1 2
- B1 3
- C2
- D3
Correct answer
D. 3
Step-by-step solution
The sum of probabilities in a probability distribution is equal to 1. 1 2 + 1 5 + 3 25 + K + 1 25 + 1 25 = 1 25 + 10 + 6 + 2 + 2 50 + K = 1 45 50 + K = 1 K = 1 - 9 10 = 1 10 The expected value E(X) is given by x_i P(x_i) . E(X) = 1 1 2 + 2 1 5 + 4 3 25 + 2A K + 3A 1 25 + 5A 1 25 = 2.94 1 2 + 2 5 + 12 25 + 2A 1 10 + 3A 25 + 5A 25 = 2.94 25 + 20 + 24 50 + A 5 + 8A 25 = 2.94 69 50 + 5A + 8A 25 = 2.94 1.38 + 13A 25 = 2.94 13A 25 = 2.94 - 1.38 = 1.56 13A = 1.56 25 = 39 A = 39 13 = 3 Answer: 3