Just a regular student: Alex, your friend and a hard-working student with anxiety is enrolled in a probability course. Raised in a perfectionist background, he is worried about quizzes messing up his grade. Each quiz is out of 5 marks and due to Alex's hard work you know that his score on each quiz can be modelled by a Uniform random variable X distributed on the interval [3.5, 5] and you know that his performance on each quiz is independent from other quizzes. The course has 12 quizzes and it isn- 2. Alex comes to you to comfort him and help him revise concepts. You decide to do both at the same time. (a) What is the probability that he will score less than 4 in a particular quiz. (b) Write the CDF for X. (c) What is the expected score (out of 30) if he gives only the first 10 quizzes. (d) he is satisfied with each quiz that is counted. (Meaning he has > 4 in at least 10 quizzes). Alex is satisfied with a quiz, if he gains at least 4 in each quiz. What is the pro bability that (e) his scores vary. What is the standard deviation for each quiz? Your friend is now comforted and goes for a break. You wonder to yourself, how much will

Just a regular student: Alex, your friend and a hard-working student with anxiety is enrolled in a probability course. Raised in a perfectionist background, he is worried about quizzes messing up his grade. Each quiz is out of 5 marks and due to Alex's hard work you know that his score on each quiz can be modelled by a Uniform random variable X distributed on the interval [3.5, 5] and you know that his performance on each quiz is independent from other quizzes. The course has 12 quizzes and it isn- 2. Alex comes to you to comfort him and help him revise concepts. You decide to do both at the same time. (a) What is the probability that he will score less than 4 in a particular quiz. (b) Write the CDF for X. (c) What is the expected score (out of 30) if he gives only the first 10 quizzes. (d) he is satisfied with each quiz that is counted. (Meaning he has > 4 in at least 10 quizzes). Alex is satisfied with a quiz, if he gains at least 4 in each quiz. What is the pro bability that (e) his scores vary. What is the standard deviation for each quiz? Your friend is now comforted and goes for a break. You wonder to yourself, how much will

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Hamza comes to office located in Islamabad through different modes of transport. From his past data, itis known that the probability of him coming through car, bus, motorbike and rickshaw are respectively 3/10,1/5,1/10,2/5The probabilities that he will arrive to his office late are 1/4,1/3,1/12 if he comes bycar, bus and motorbike. Interestingly, he will not be late if he comes by rickshaw. Suppose, he arriveslate on Friday. What is the probability that he came by car?
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