Concept explainers
A manufacturer guarantees a product for 1 year. The time to failure of the product after it is sold is given by the probability density function
Where t is time in months. What is the probability that a buyer chosen at random will have a product failure
- (A) During the warranty period?
- (B) During the second year after purchase?
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
EP CALCULUS FOR BUSINESS..-MYLAB ACCESS
- part D E needarrow_forwardDaily total solar radiation for a specified location in Florida in October has probability densityfunction given byf (y) =$ (3/32)(y − 2)(6 − y), 2 ≤ y ≤ 6,0, elsewhere,with measurements in hundreds of calories. Find the expected daily solar radiation for October.arrow_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_forward
- Q5arrow_forward4. "Time headway" In highway traffic flow the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point is called time headway. Now, let X = the time headway for two randomly chosen consecutive cars on a highway during a period of heavy traffic flow. The following probability density function of X is suggested by traffic experts: f(x) = 0.15*e-0.15(x-0.5) for (x ≥ 0.5 sec) 0 otherwise a. Draw f(x) from x = 0 to x= 10 sec. b. Find P(X ≤ 5 sec) and show it on the figure you have drawn. c. What is E[X] and Var[X] ? d. Find Cumulative Distribution Function of X.arrow_forwardShow complete and step by step solution.arrow_forward
- 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.arrow_forwardA company uses wood chips in the manufacture of processed wood pieces of various sizes. Suppose the tons of wood chips T used per day has a probability density function f(T) = 0.25e-0.25T (a) Find the probability of using more than 4 tons of wood chips in a day. (Round your answer to three decimal places.) (b) Find the number of tons 7 (to the nearest ton) so that the probability of using more than 7 tons in a day is 0.07. tonsarrow_forwardThe yearly cost in millions of dollars caused by Godzilla rampaging in Tokyo is a random variable with an exponential probability density functionf(x) = 0.45e−0.45x, [0, ∞) Find the median yearly cost (in millions of dollars) of Godzilla’s rampages.arrow_forward
- Q1. 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_forwardA transmission repair firm that wants to offer a lifetime warranty on its repairs has determined that the probability density function for transmission failure after repair is shown below, where t is the number of months after repair. (Round your answers 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?arrow_forward. Let the waiting time 'w' has a gamma distribution with a = k and b = 12. Write the corresponding probability density function and also obtain the average waiting time.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage