I have persuaded Msc degree in Statistics from Bangalore University securing the first ranking. Statistics and Mathematics are my favourite subjects and I love to keep on spending time reading them.
Insect Fragments The Food and Drug Administration sets a Food Defect Action Level (FDAL) for the various foreign substances that inevitably end up in the food we eat and liquids we drink. For example, the FDAL level for insect filth in peanut butter is 0.3 insect fragment (larvae, eggs, body parts, and so on) per gram. Suppose that a supply of peanut butter contains0.3 insect fragment per gram. Compute the probability that the number of insect fragments in a 5 -gram sample of the peanut butter is(a) exactly two. Interpret the result.(b) fewer than two. Interpret the result.(c) at least two. Interpret the result.(d) at least one. Interpret the result.(e) Would it be unusual for a 5 -gram sample of this supply of peanut butter to contain four or more insect fragments?
Wendy's Drive-Through Cars arrive at Wendy's drive-through at a rate of 0.2 car per minute between the hours of 11: 00 P.M. and 1: 00 A.M. on Saturday evening. Wendy's begins an advertising blitz that touts its late-night service. After one week of advertising. Wendy's officials count the number of cars, $X$, arriving at Wendy's drive-through between the hours of 12.00 midnight and 12: 30 A.M. at 200 of its restaurants. The results are shown in the following table:(a) Construct a probability distribution for the random variable$X,$ assuming it follows a Poisson process with $\lambda=0.2$ and $t=30 .$ This is the probability distribution of $X$ before the advertising.(b) Compute the expected number of restaurants that will have 0 arrivals, 1 arrival, and so on.(c) Compare these results with the number of arrivals after the advertising Does it appear the advertising was effective? Why?
Quality Control A builder ordered two hundred 8 -foot grade A 2 -by- 4 s for a construction job. To qualify as a grade A board, each 2 -by- 4 will have no knots and will average no more than 0.05 imperfection per linear foot. The following table lists the number of imperfections per 2 -by- 4 in the 200 ordered: (a) Construct a probability distribution for the random variable$X,$ the number of imperfections per 8 feet of board, assuming that it follows a Poisson process with $\lambda=0.05$ and $t=8.$(b) Compute the expected number of 2 -by- 4 s that will have 0 imperfections, 1 imperfection, and so on.(c) Compare these results with the number of actual imperfections. Does it appear the 2 -by- 4 s are of grade A quality? Why?
Find the cumulative distribution function of the random variable $W$ in Exercise 3.8 . Using $F(w),$ find(a) $P(W>0)$(b) $P(-1 \leq W<3)$.
Let $X_{1}, X_{2}, \ldots, X_{n}$ represent a random sample from each of the distributions having the following pdfs:(a) $f(x ; \theta)=\theta x^{\theta-1}, 0<x<1,0<\theta<\infty$, zero elsewhere.(b) $f(x ; \theta)=e^{-(x-\theta)}, \theta \leq x<\infty,-\infty<\theta<\infty$, zero elsewhere. Note that thisis a nonregular case.In each case find the mle $\hat{\theta}$ of $\theta$.
Calculate the eigenvalues and the corresponding eigenvectors of the given matrix. All matrices have integer eigenvalues
{{0,-2,1}, {-7,-1,3}, {-11,2,4}}
If the total cholesterol values for a certain population areapproximately normallydistributed with a mean of 200 mg/100 ml and a standard deviationof 20 mg/100 ml, find theprobability that an individual picked at random from thispopulation will have a cholesterolvalue:(a) Between 180 and 200 mg/100 ml (b) Greater than 225 mg/100 ml(c) less than 150mg/100 ml (d) Between 190 and 210 mg/100 ml.
Let X and Y each have the distribution of a fair six-sided die,and let Z = X + YZ=X+Y.What is E[X|Z]? (Expected value of X given Z)
6.14 The finished inside diameter of a piston ring is normallydistributed with a mean of 10 centimeters and a standard deviationof 0.03 centimeter. (a) What proportion of rings will have insidediameters exceeding 10.075 centimeters? (b) What is the probabilitythat a piston ring will have an inside diameter between 9.97 and10.03 centimeters? (c) Below what value of inside diameter will 15%of the piston rings fall?
Scores on an English test are normally distributed with a meanof 37.6 and a standard deviation of 7.6. Find the score thatseparates the top 59% from the bottom 41%
Computer technology has produced an environment in which robots operate with the use of microprocessors. The probability that a robot fails during any 6-hour shift is 0.10. What is the probability that a robot will operate through 5 shifts before it fails? Select one: 0.36 0.94 0.059 0.065
