Assignment: Homework 8

University:
California State University, Northridge
Course:
MATH 340 | Introduction to Probability and Statistics
Academic year:

2023
Views:

58

Pages:

4
Author:

Samuel K

HW08-Nyi Nyi Moe Htet Student: Nyi Nyi Moe Htet Date: 12/03/23 Instructor: Xiaolong Han Course: CSUN_MATH340_HAN (1) Assignment: HW08 1. Suppose that X is a random variable with mean and variance both equal to 40. What can be said about P{0 < X < 80}? 39 P{0 < X < 80} ≥ 40 (Simplify youranswer.) 2. From pastexperience, a professor knows that the test score of a student taking her final examination is a random variable with mean 76. ( a) Give an upper bound for the probability that astudent's test score will exceed 78. (b) Suppose, inaddition, that the professor knows that the variance of astudent's test score is equal to 8. What can be said about the probability that a student will score between 72 and 80? (c) How many students would have to take the examination to ensure with probability at least 0.9 that the class average will be within 2 of 76? Do not use the central limit theorem. (a) An upper bound for the probability is 38 . 39 (Simplify youranswer.) (b) The probability is greater than or equal to 1 2 . (Simplify youranswer.) (c) At least 20 students would have to take the examination. (Type a wholenumber.) 1/4 12/3/23, 3:36 PM HW08-Nyi Nyi Moe Htet 3. Let X1 , X2 , ..., X22 be independent Poisson random variables with mean 1. 22 (a) Use the Markov inequality to obtain a bound on P ∑ Xi > 11 . 1 22 (b) Use the central limit theorem to approximate P ∑ Xi > 11 . 1 1 Click the icon to view the standard normal curve table. 22 (a) Using the Markovinequality, P ∑ Xi > 11 11 ≤ 6 1 . (Type an integer or a simplifiedfraction.) 22 (b) Using the central limittheorem, P ∑ Xi > 11 ≈ 0.9875 . 1 (Round to four decimal places asneeded.) 1: Standard Normal Curve Table 2/4 12/3/23, 3:36 PM HW08-Nyi Nyi Moe Htet 3/4 12/3/23, 3:36 PM HW08-Nyi Nyi Moe Htet 4. A person has 196 light bulbs whose lifetimes are independent exponentials with mean 5 hours. If the bulbs are used one at atime, with a failed bulb being replaced immediately by a newone, approximate the probability that there is still a working bulb after 1036 hours. 2 Click the icon to view the standard normal curve table. The probability is approximately 0.2119 . (Round to four decimal places asneeded.) 2: Standard Normal Curve Table 5. This question has been removed from this assignment by your instructor; you have received full credit. 4/4