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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.1: Continuous Probability Models

Problem 8E

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Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
Suppose that the probability density function of the length of computer cables is f (x) = 2x/(52) for x between 0 and 5 meters. Determine the standard deviation of the cable length. Please enter the answer to 2 decimal places.
Suppose that the probability density function of the length of computer cables is f (x) = 2x/(32) for x between 0 and 3 meters. Determine the mean of the cable length. Please enter the answer to 2 decimal places.
Bill has researched that the life expectancy (in months) of Bluedenia plants is a continuous random variable with probability density function (pdf) given by f(x) = (1/36)[6x - x^2] for x between 0 and 6 and 0 otherwise. a. What is the probability that one of these plants survives for at most 5 months? Your answer should be correct to 3 places after the decimal point. %3D b. What is the expected value of the random variable; that is the mean life expectancy? Your answer should be correct to 3 places
The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf. What is the probability that the actual weight is within 0.4 g of the prescribed weight?
The lifetime of an aquatic insect has an exponential disribution with parameter θ = 10 hrs. (i) What is the probability that an aquatic insect lives longer than 12 hrs? (ii) What is the median of this distribution? (50% live less time and 50% live longer) (iii) Assume the lifetimes of these insects are independent of each other. What is the probability that at least 35 of the next 100 insects live longer than 12 hrs?
For a particular kind of battery, the probability density function for x hours to be the life of a battery selected at random is given by -x/60 x > 0 f(x) = - 60 0, x < 0 Find the probability that the life of a battery selected at random will be between 15 and 25 hours.
For a continuous pdf, the probability of an exact value can be found . Is this true or false ?
Consider the random variable with a probability density function of f(x)= (1/x ln(1.5)), 4<=x<=6 and f(x) = 0 elsewhere. What is the expected value of this random variable? What is the median of this random variable?
The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) = (e-x/1000 )/1000 for x > 0. Determine the the number of hours at which 12% of all components have failed. Please enter the answer to 2 decimal places.
The probability density function of the length of a metal rod is f(x) = 2.0 for 2.3
If X = ln Y has a normal distribution with the mean μand the standard deviation σ, find the probability densityof Y which is said to have the log-normal distribution.

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A test instrument needs to be calibrated periodically to prevent measurement errors. After some time of use without calibration, it is known that the probability density function of the measurement error is f(x)=1.0(1-0.5x) for 0