A discrete random variable X has the following probability distribution. What…
2021
A discrete random variable X has the following probability distribution. What is the value of K?
- A.
1/30
- B.
1/40
- C.
1/10
- D.
1/20
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Rule: The sum of all probabilities in a discrete probability distribution must be 1.
Summing the probabilities: K + 2K + 2K + 3K + K^2 + 2K^2 + (7K^2 + K) = 1.
Combine terms: (1 + 2 + 2 + 3 + 1)K + (1 + 2 + 7)K^2 = 1 => 9K + 10K^2 = 1.
Quadratic equation: 10K^2 + 9K - 1 = 0.
Factorize: 10K^2 + 10K - K - 1 = 0 => 10K(K + 1) - 1(K + 1) = 0 => (10K - 1)(K + 1) = 0.
Solutions: K = 1/10 or K = -1. Since probability cannot be negative for K, we use K = 1/10.
Final Answer: Option 1 (1/10)