Concept explainers
Product life. The life expectancy (in years) of an automobile battery is a continuous random variable with probability density function given by
Find the median life expectancy.
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardPopulation 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?arrow_forwardIf the probability density function of the random variable X is eX, x>0, f(x)= 0, Otherwise. Then the variance of X is Select one: О a.2 O b.1 O c. -2 d. -1arrow_forward
- The repair time (in hours) for a certain machine is a random variable with probability density function (xe S(x) = What is the probability that the repair time is less than 2 hours? b. a. What is the probability that the repair time is between 1.5 and 3 hours? Find the mean repair time. d. C. Find the cumulative distribution function of the repair times.arrow_forwardThe probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)arrow_forwardQ. 2 Suppose I see students during regular office hours. Time spent with students follow an exponential distribution with mean of 20 minutes. (i) Write the probability density function of random variable X, E (X) and Var(X). (ii) Find the probability that a given student spends less than 0.4 hours with the professor. (iii) Find the probability that a given student spends between 0.20 and 0.5 hours with the professor. (iv) Find the probability that a given student spends at least 0.75 hours with the professor.arrow_forward
- The length of life X, in days, of a heavily used electric motor has probability density function f(x) = {0, -3x S3e x20 %3D otherwise Find the probability that the motor has at least 1/2 of a day, given that it has lasted 1/4 of a day. Find the mean and the variance for X.arrow_forwardConsider random variable X that is exponentially distributed with E(X) = 2. Select the probability density function for X. O f(z) = e- O f(r) = 2e-2 O F(r) = 1-e-- O F(x) = 1-e-25arrow_forwardThe probability density function of X discrete random variable given in the photograph is given. Find the expected value, variance and standard deviation of X.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning