Concept explainers
Product warranty. A manufacturer warrants a product for parts and labor for 1 year and for parts only for a second year. The time to a failure of the product after it is sold is given by the probability density function
What is the probability that a buyer chosen at random will have a product failure
(A) During the first year of warranty?
(B) During the second year of warranty?
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
EP CALCULUS FOR BUSINESS..-MYLAB ACCESS
- 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.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_forwardQ1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . . (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.arrow_forward
- answer only part b .arrow_forwardLet random variable X be the length of the side of a square. Let Y be the area of the square, i.e. Y =X?. Suppose that X has the probability density function, (3x?if 0arrow_forward1 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.arrow_forwardLet the probability density function of the random variable X be given as (pdf). Event A = | X - b | <a / 2. a = 0.6 and b = 0.3. Under the condition A of the random variable XFind the probability density function.arrow_forwardFind a and b plsarrow_forwardThe pH water samples from a specific lake is a random variable X with probability density function. f(x) = {8 (7– x)², 5 < x<7 0, elsewhere a. ) Find E(X) ( expected value or mean) b. ) Find V(X) ( Variance)arrow_forwardStast 2.arrow_forwardA continuous probability distribution has probability density function f (y) = a (b– y), 0< y < b, and 0 elsewhere. If the mean of the distribution is .2, find the values of a and b a = 1/9 and b= 2) a = 1/72 and b = 12 O a = 1/18 and b= 6 0 a = 2/9 and b = 30 a = 2/81 and b = 90arrow_forwardRadioactive mass 1 emits particles at a mean rate of 1, per second, and radioactive mass 2 emits particles at a mean rate of 2 per second. Mass 1 is selected with probability p, and mass 2 is selected with probability 1 - p. Let X be the time at which the first particle is emitted. It can be shown that X has a mixed exponential distribution with probability density function SPhieh+(1- p)Àze* S(x) = x > 0 a. Find Hx- b. Find the cumulative distribution function of X. C. Let 11 = 2, 12 = 1, and p = 0.5. Find P(X < 2). d. Let X, = 2, X, = 1, and p = 0.5. Given that P(X < 2), find the probability that mass 1 was selected.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill