Concept explainers
Product warranty. Graph the probability density function for Problem 44 over the interval [0, 3], interpret part (B) of Problem 44 geometrically, and describe the geometric representation.
44. Product warranly. 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
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forward. Find each probability.(a) X ∼ Gaussian (0, 3). Find P[X > 4.5].(b) Y ∼ Gaussian (50, 10). Find P[X < 75]arrow_forward2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, f(t) = This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t = a and t = b. A related function is 2 F(1) = e2/9 dt, r20. This function gives the probability that the day's temperature is between t = -x and t = r different from the monthly average temperature. For example, F(1) = (0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(r) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the monthly average.…arrow_forward
- Problem 3.9: The speed distribution function for N particles in a fixed volume is given by: AV (B-V) B3 where V (> 0) is the particle speed, and A and B are positive constants. Determine: (a) The probability density function F(V). (b) The number of particles N in the volume. (c) The minimum speed Vmin and maximum speed Vmax. (d) The most probable speed where the probability density function is the largest. (e) The average speed V and the root-mean-square average speed Vrms = √V² f (V) =arrow_forward1. Suppose that for a certain life the probability density function is x (*) 1+x ,x >0 X. Find (i) the survival function ofx (ii) the probability that the life aged 25 will die within next 15 years. (iii) the probability that the life aged 42 will die between 55 and 62.arrow_forward2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, 1 f(t) = %3D e This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t = a and t = b. A related function is 2 F(2) = e-t /9 dt, x >0. x > 0. This function gives the probability that the day's temperature is between t = -x and t = x different from the monthly average temperature. For example, F(1) 2 0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(x) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the…arrow_forward
- H3.arrow_forwardProblem 4. Let fx (x) be the probability density function of X, which is given by fx(x) = - -2x ce 0, " x > 2 otherwise (a) Find the value of c to make ƒx a valid probability density function. (b) Calculate the cumulative distribution function (c.d.f.) of X. (c) Calculate P(12 < X ≤ 25) using the c.d.f. from part (b). You do not need to simplify your answer.arrow_forwardProblems 4.2. Suppose that X is a continuous random variable with probability density function given by f(x) = x² + x + } for 0arrow_forwardRecommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning