2013 The following problems have been selected from the course text. 4.78 In a large collection of wires‚ the length of a wire is X‚ an exponential random variable with mean 5π cm. Each wire is cut to make rings of diameter 1 cm. Find the probability mass function for the number of complete rings produced by each length of wire. 4.85 The exam grades in a certain class have a Gaussian pdf with mean m and standard deviation σ. Find the constants a and b so that the random variable Y = aX +
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F-2‚Block‚ Amity Campus Sec-125‚ Nodia (UP) India 201303 ASSIGNMENTS PROGRAM: SEMESTER-I Subject Name : Study COUNTRY : Permanent Enrollment Number (PEN) : Roll Number : Student Name : INSTRUCTIONS a) Students are required to submit all three assignment sets. ASSIGNMENT DETAILS MARKS Assignment A Five Subjective
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thought to be 20%. What is the average (total) cost of this overbooking policy? What does this mean? Why is this different to the £6‚250 Caroline’s processor estimated? What is the probable range of total cost (95% confidence)? What is the probability that the (total) cost will exceed £15‚000? Now evaluate the overbooking policy you recommended in Section 2 (using the same criteria). Also evaluate the (total) costs of a policy of not overbooking at all‚ a practice that is employed
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s factorial = 2 Number of servers 2 P(0) = 0.2 0.533333333 2 Utilization 66.67% n Pn 1 2 P(0)‚ probability that the system is empty 0.2000 0 1 0.2 0.2 1 2 Lq‚ expected queue length 1.0667 1 1.333333333 0.266666667 0.266666667 1 2 Ls‚ expected number in system 2.4000
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After that‚ these needed rainfall amounts with the rainfall in Big Melen River was compared. Finally‚ “Mann-Kendall Test” was applied on both of the cities’ stations to find out if there is a trend. As a result‚ by defining these data as a probability density function‚ the longest periods of the drought and the rainfall needed on these times were calculated. The trends (increasing and decreasing) were seen in these both regions. These results are in agreement with the other drought and trend
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Table 2A and 3B 3A) we performed A priori chi-square test for these two tables. The main reason for the chi-square is to find out if the expected value is any different from the observed value. This part of the observation tested the null hypothesis‚ which states that‚ if when Ear#1(which was test-crossed kernel) is counted and approves of the Mendelian expectation of 1:1:1:1 phenotypic ratio. The chi-square for this data was excepted to accept the null hypothesis. The reason that it was expected
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personal computers are randomly selected‚ what is the probability that at most five of the personal computers are upgraded? How many upgraded personal computers would you expect if 60 personal computers are selected at random and what is the standard deviation? (4 marks) ii) b) Suppose that the number of flaws in sheets of anodized steel follows a Poisson distribution with an average of two flaws in a 20 square meter area. i) What is the probability that there will be less than one flaw in a ten
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Problem 1 A gas station with only one gas pump employs the following policy: if a customer has to wait‚ the price is $3.50 per gallon; if they don’t have to wait‚ the price is $4.00 per gallon. Customers arrive according to a Poisson process with a mean rate of 20 per hour. Service times at the pump have an exponential distribution with a mean of 2 minutes. Arriving customers always wait until they can by gasoline. Determine the expected price of gasoline per gallon. Problem 3 The Old Colony theme
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regression line Week 5 (9/24‚ 9/26) • QUIZ 2 on Monday 9/23 on Chapters 5‚ 8‚ 9 (in lab) • Reading: chapters 13‚ 14‚15; SG 12‚ 17‚ 18‚ 19 • Probability‚ conditional probability‚ Bayes’ rule‚ binomial distribution Week 6 (10/1‚ 10/3) • Reading: chapter 15; SG 20‚ Notes on chance variables by Prof. Roger Purves • Continue probability‚ some discrete distributions (geometric‚ negative binomial‚ hypergeometric). Week 7 (10/8‚ ‚10/10) • MIDTERM 1 on Tuesday 10/8 on Chapters 1-5‚ 8-15
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estimate the probabilities of uncertain events. For example‚ what is the probability that a new product’s cash flows will have a positive net present value (NPV)? What is the risk factor of our investment portfolio? Monte Carlo simulation enables us to model situations that present uncertainty and then play them out on a computer thousands of times. NOTE The name Monte Carlo simulation comes from the computer simulations performed during the 1930s and 1940s to estimate the probability that the chain
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