CHAPTER 4 TUTORIAL SET QUESTIONS.pdf

CHAPTER 4 TUTORIAL SET QUESTIONS 1. Consider the following discrete probability distribution table below. x 0 1 2 3 4 P ( x) 1/5 1/5 1/5 1/5 1/5 Determine the expected value and variance of the discret...

CHAPTER 4 TUTORIAL SET QUESTIONS 1. Consider the following discrete probability distribution table below. x 0 1 2 3 4 P ( x) 1/5 1/5 1/5 1/5 1/5 Determine the expected value and variance of the discrete random variable. 2.A normal 6-sided fair die is thrown 24 times and the number of 6’s scored is recorded. Calculate the mean and the variance. 3. The random variable 𝑋 takes values −1, 0, 1 with probabilities 1,2 5 , respectively. 8 8 8 a. Compute the 𝐸(𝑋). b. Give the pmf of 𝑌 = 𝑋2 and use it to compute 𝐸(𝑌). Compute 𝑉𝑎𝑟(𝑋). 4. A discrete random variable X has the following probability mass function (PMF): 𝑐𝑥 𝑓𝑜𝑟 𝑥 = 1,2,3,4. 1 𝑃𝑟(𝑋 = 𝑥) = { 𝑓𝑜𝑟 𝑥 = 5 2 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 a. Find the value of the constant 𝑐. b. Find the 𝐸(3𝑋 + 2). Find the 𝑉𝑎𝑟(3𝑋 + 2). 5. 3.Let 𝑋~𝑃𝑜(0.2). determine the following probabilities: a.𝑃𝑟(𝑋 ≤ 3). b.𝑃𝑟(𝑋 = 6). c.𝑃𝑟(𝑋 > 0). 4. Suppose 𝑋~𝐵(𝑛 = 10, 𝑝 = 0.5), determine the following probabilities: a.𝑃𝑟(𝑋 ≤ 2). b.𝐸(𝑋) and 𝑉𝑎𝑟(𝑋).