1The time to failure, t, in hours, of a machine is often exponentially distributed with a probability density function f(t)=ke-kt, 0≤t<∞o, where k = — and a isathe average amount of time that will pass before a failure occurs. Suppose that the average amount of time that will pass before a failure occurs is 80 hr. Whatis the probability that a failure will occur in 52 hr or less?The probability is(Round to four decimal places as needed.)

Given problem Given that Probability density function : f( t ) = k e -kt ; 0 ≤ t ≤ ∞ k =…

Answered: The time to failure, t, in hours, of a…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 56SE: Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such...

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Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .
A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.
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Suppose the unknown X satisfies −2 ≤ x ≤ 2 and has the probability density function fX (x)=C (4−x^2),−2 ≤ x ≤ 2 ,where C is a constant. What is the probability that |X| ≥ 1? Possible Answers: 10/16 21/32 5/16 3/32
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