29. The time until a chemical reaction is complete (in milliseconds) is approximated by the cumulative distribution functionx <0F (x) = { ,1-e-0.01zx >0The probability that a reaction completes within 250 milliseconds isO 0.9179O 0.0082O 0.0821O 0.0918

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.
Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?
Let the random variable X be the portion of a flood insurance claim for flooding damage to a house. The probability density of X has the form f(x)= c(3x2 - 8x - 5) for 0 < x < 1. What is the value of the constant c? What is the cumulative distribution function of X?
The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with a pdf of f(x)=1/162(x-3)^2(x+6) for 0 < x < 6What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?Answer to four decimal places What is the probability of a widget being made later than 1.3 s?Answer to four decimal places
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The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has cumulative distribution F with the following definition:F(x) = 0 for x < 1 and F(x)= (3/2)-(3/2x) for 0 ≤ x ≤ 3 a) What is the probability density function for X for 1 ≤ x ≤ 3? f(x) = .5 f(x) = (3/4x^2) f(x) =(3/2x^2) f(x) = (3/2)-(3/2x) f(x) = (3x/2x^3) b) What is the probability that X > 2? c) What is the probability X < 2 ? d) What is the probability that X > 2.5? e) What is the probability that X > 3? f) What is the probability that X > 2.5 given the X > 2? g) Calculate the 60th percentile of X. h) What is the expected value of X? i) What is the expected value of X2 j) What is the variance of X? k) What is the probability that X is more than 0.1 above its expected value?
X1 and X2 are two discrete random variables, while the X1 random variable takes the values x1 = 1, x1 = 2 and x1 = 3, while the X2 random variable takes the values x2 = 10, x2 = 20 and x2 = 30. The combined probability mass function of the random variables X1 and X2 (pX1, X2 (x1, x2)) is given in the table below a) Find the marginal probability mass function (pX1 (X1)) of the random variable X1.b) Find the marginal probability mass function (pX2 (X2)) of the random variable X2.c) Find the expected value of the random variable X1.d) Find the expected value of the random variable X2.e) Find the variance of the random variable X1.f) Find the variance of the random variable X2.g) pX1 | X2 (x1 | x2 = 10) Find the mass function of the given conditional probability.h) pX2 | X1 (x2 | x1 = 2) Find the mass function of the given conditional probability.i) Are the random variables X1 and X2 independent? Show it. The combined probability mass function of the random variables X1 and X2 is below

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The time until a chemical reaction is complete (in milliseconds) is approximated by the cumulative distribution function F(z) = { ," x <0 I-e-0.01z x >0 The probability that a reaction completes within 250 milliseconds is O 0.9179 O 0.0082 O 0.0821 O 0.0918