FALL SEMESTER 2020 MTH 2210-C: INTRODUTION TO APPLIED STATISTICS INSTRUCTOR: DR. GABRIEL OKELLO DATE: NOVEMBER 19, 2020 INDIVIDUAL EXERCISE TWELVE INSTRUCTIONS Attempt All Questions 1. The probability distribution for a random variable 𝑋 follows: 𝑃(𝑥) 0.20 0.15 0.25 0.40 𝑥 20 25 30 35 a. Is this probability distribution valid? Explain b. What is the probability that 𝑋 is greater than 25? c. Find the expected value and standard deviation of 𝑋. 2. A random variable 𝑋 has the following probability distribution 𝑥 𝑝(𝑥) 0 1 𝑎 2 3𝑎 3 5𝑎 4 7𝑎 9𝑎 a. Determine the value of 𝑎 b. Find 𝑃(𝑋 < 4), 𝑃(𝑋 ≥ 2), 𝑃(1 < 𝑋 < 6) 5 11𝑎 6 13𝑎 7 15𝑎 8 17𝑎