Answered: The length of time required by students…

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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I. The length of time required by students to complete a 1-hour exam is a random variable X (in hours) with probability density function f(x) = 45(x3 + 1) for 0 < x < 1 and f(x) = 0 for x • • • • • • otherwise. Randomly select a student from this class. Whatistheprobabilitythatthecompletiontimeforthisstudentisatleast50minutes? Note that 40 minutes is equal to 40/60 hr. What is the probability that completion time is between 20 and 40 minutes? Determine the mean and variance of completion time. What is the CDF Graph the CDF Graph the PDF II . The average American eats 2,000 calories per day with a standard deviation of 500 calories. If this distribution follows a normal distribution, (a) What is the probability that someone eats between 2,000 and 3,000 calories per day? (b) How many calories corresponds to the 70th percentile? III. Draw a picture (Venn Diagram) for the following distributions. Additionally, find the fol- lowing probabilitis if P(A) = 0.4 and P(B) = 0.3 and P(A ∩ B) = 0.1 (a) P(A) (b) P(B) (c) P(A∪B) (d) P(A′ ∪B) (e) P(A∪B′) (f) P(A′ ∪B′) (g) P(A∩B) (h) P(A′ ∩B) (i) P(A∩B′) (j) P(A′ ∩B′) IV. Suppose X1 and X2 are two independent random variables with the following density func- tion: f(x)= { if0 1)]

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