A transmission repair firm that wants to offer a lifetime warranty on its repairs has determined that the probability densityfunction for transmission failure after repair is shown below, where t is the number of months after repair. (Round youranswers to three decimal places.)f(t) = 0.3e-0.3t(a) What is the probability that a transmission chosen at random will last 5 months or less?(b) What is the probability that a transmission chosen at random will last more than 5 months?

probability that it will last 5 or less months

Answered: A transmission repair firm that wants…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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1 The time between major earthquakes in the Taiwan region is a random variable with probability density function f(t) = -t/3650.1 where t is measured in days. 3650.1 A. Find the probability that the time between a major earthquake and the next one is more than 2 years but less than 6 years. B. Find the probability that the time between a major earthquake and the next one is more than 8030 days.
x is a gaussian random variable with a PDF as described above, where μ is the mean, σ is the standard deviation , and Fx(X) refers to the cumulative distribution function CDF. It is known that Fx(-0.7) = 0.500 and Fx(1.3)=0.841, what value of Xo do we find the probability Fx(Xo) = P(X<Xo) = 0.023 ?
Q. 6 Find 30th percentile, median and 70th percentile for the following probability density functions: X < 0 0s X < 1 0s X s 1.3 1.3 (i) fx(x) = 3x2 1s Xs 2 (ii) fx(x) = %3D %3D 2-x 1.3 < X s 2 14 otherwise 0.7 otherwise
It is known that the probability distribution given a random variable Y with the parameter θ belongs to the Exponential Family of distributions if we can write f(y;θ) as the following in the picture attached. Given the picture attached, answer all parts a, b, and c of the question. Show all work and all steps.
Which statements below are true for a probability distribution function (pdf), f(x)? The total area under f(x) is equal to 1. f(x) is non-decreasing f(x) is a probability f(x) is non-negative x is non-negative
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Suppose that a random variable X has the following probability density function. SC(36-x²) 0 ≤ x ≤ 6 otherwise f(x) = {C (² Find the expected value of X. (You will need to find the value of the constant C so that f is a pdf.)
For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. f(x) = 195x, (0,5] 2, [0,5] 125 a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. O = (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)
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The Gamma distribution is often used to describe the wait time until a certain number of events occurs. Assume x1, . . . , xn ∼iid Gamma(α, β), where α is shape and β is rate. Calculate the maximum likelihood estimator of β either by hand or via R, but not both. The probability density function (PDF) for the Gamma distribution is: Calculate the log-likelihood function of the function below. I t doesnt have to be on r studi you can do by your hand
Question 2: Suppose we have a random sample X₁, X2,..., X, from the following probability density function: f(x;0) 1 - e 20 -1/(20), x>0, 0>0 Derive the maximum likelihood estimator of 0. Be sure to check the second derivative.

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