Problem 1. Consider a family of 1-dimensional class-conditional densities given by:p(r|w;) =604expwhere 0; is the parameter corresponding to class wi.(a) Given independent samples r1, #2, · ·· ,In from class wi, find the maximum like-lihood estimate of 0;.(b) Suppose that we have two classes, i.c., C = 2. We have observed the samplesDi = {1,2,6, 7} from class wi and D2 = {9,13, 14} from class w2. ASsuming thatP(wi) = and using the maximum likelihood estimates of 01 and 02, find theBayes' classifier and determine the decision regions R1 and R2.

Given: p(x|wi)=x36θi4exp-xθi, x≥0 to find mle of θi

Answered: Problem 1. Consider a family of…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter29: Tolerance, Clearance, And Interference

Section: Chapter Questions

Problem 9A: Refer to Figure 29-7. Dimension A with its tolerance is given in each of the following problems....

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Problem 3: car-planes and city size. Consider a regional economy with 12 million workers and an urban utility curve of u(n) = 15 + 12n − 2n2, where n is the number of workers in millions. Initially the region has four cities, each of the same size. Suppose city A introduces carplanes to replace regular cars for commuting and its urban utility function is u(n) = 15 + 12n − n2. Predict the effect of the carplane on the equilibrium distribution of population between cities the equilibrium utility level and regional utility.
Answer question #9. Show the graph of the rejection region.
Problem#1: On the desk of an office of a Banking Company, the arrivals of the customers follow poisson law and an average at every 10 minutes a customer arrives. The officer responsible takes on an average 6 minutes to serve a customer, assuming the exponentially distributed. Find out the average arrival rates for(a) 1 hour(b) 15 minutes(c) 8 hours
J 1 Problem 126. Let X and Y be discrete random variables with joint probability mass function pX,Y (x, y) = C/[(x + y − 1)(x + y)(x + y + 1)], x, y = 1, 2, 3, . . . Determine the marginal mass functions of X and Y
Problem 1. A continuous random variable X is defined by f(x)=(3+x)^2/16 -3 ≤ x ≤ -1 =(6-2x^2)/16 -1 ≤ x ≤ 1 =(3-x^2)/16 -1 ≤ x ≤ 3 a)Verify that f(x) is density. b)Find the Mean
Figure 6.4b (p. 172) plotted the sampling distribution of the mean from 200 samples of size 5 from the population of 1000 birthweights given in Table 6.2. The mean of the 1000 birthweights in Table 6.2 is 112.0 oz with standarddeviation 20.6 oz. A) If the central-limit theorem holds, what proportion of the sample means should fall within 0.5 lb of the population mean (112.0 oz)? B) Answer Problem 6.52 for 1 lb rather than 0.5 lb. C) Compare your results in Problems 6.52 and 6.53 with the actual proportion of sample means that fall in these ranges. D) Do you feel the central-limit theorem is applicable for samples of size 5 from this population? Explain.
Question 15 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 3 human errors on any given day? State your answer as a decimal value rounded to two digits after the decimal point.
Question 13 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 3 technical errors on any given day? State your answer as a decimal value rounded to two digits after the decimal point.
Question 10 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 0 technical errors given 3 human errors? State your answer as a decimal value rounded to two digits after the decimal point.
Problem 5 Suppose {Xn}n≥0 is a DTMC, having state space S and transitionmatrix P, where S = {0,1,2,...,n}and the elements of Psatisfy the following conditions:p(0,1) = r, p(0,n) = 1 −r, p(n,0) = 1 and for each integer i ∈{1,2,...,n −1}, p(i,i + 1) = 1. Find the stationary distribution of this DTMC.
Problem 3. Suppose a test for detecting a certain rare disease has been perfected that is capable of discovering the disease in 97% of all afflicted individuals. Suppose further that when it is tried on healthy individuals, 5% of them are incorrectly diagnosed as having the disease. Finally, suppose that when it is tried on individuals who have certain other milder diseases, 10% of them are incorrectly diagnosed. It is known that the percentages of individuals of the three types being considered here in the populations at large are 1%, 96%, and 3%, respectively. Calculate the probability that an individual, selected at random from the population at large and tested for the rare disease, actually has the disease if the test indicates he is so afflicted.
Refer to Figure 29-7. Dimension A with its tolerance is given in each of the following problems. Determine the maximum dimension (maximum limit) and the minimum dimension (minimum limit) for each. a. Dimension A =4.6400.003+0.003 maximum________ minimum________ b. Dimension A =5.9270.0012+0.0000 maximum________ minimum________ c. Dimension A =2.0040.004+0.000 maximum________ minimum________ d. Dimension A =4.67290.0012+0.0000 maximum________ minimum________ e. Dimension A =1.08750.0000+0.0009 maximum________ minimum________ f. Dimension A =28.16mm0.06mm+0.00mm maximum________ minimum________ g. Dimension A =43.94mm0.00mm+0.04mm maximum________ minimum________ h. Dimension A =118.66mm0.00mm+0.07mm maximum________ minimum________ i. Dimension A =73.398mm0.012mm+0.000mm maximum________ minimum________ j. Dimension A =45.106mm0.000mm+0.009mm maximum________ minimum________

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