Hi i am having a difficult time with this problem and the parts that come along with it, Can you please do this problem step by step and can you label the parts as well. 3.1-15. The life X (in years) of a voltage regulator of a car has the pdff(x)=3x²732-(2/7)³0 < x <∞.a. What is the probability that this regulator will last at least seven years?b. Given that it has lasted at least seven years, what is the conditional probabilitythat it will last at least another 3.5 years?

Let X be the life of a voltage regulator of the car (in years). The PDF of X is given…

3.1-15. The life X (in years) of a voltage regulator of a car has the pdf f(x) = 3x² 73 e-(2/7)3 0 < x <∞. a. What is the probability that this regulator will last at least seven years? b. Given that it has lasted at least seven years, what is the conditional probability

3.1-15. The life X (in years) of a voltage regulator of a car has the pdf f(x) = 3x² 73 e-(2/7)3 0 < x <∞. a. What is the probability that this regulator will last at least seven years? b. Given that it has lasted at least seven years, what is the conditional probability

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 9E

See similar textbooks

Similar questions

Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t) be the size of the population at time t. (a) Write a formula for n(t) in terms of the doubling time a. (b) Write a formula for n(t) in terms of the relative growth rate r.
Find the positive geometric mean between 4 and 64.
Suppose that the length of time spent by a student with a professor during office hours in minutes is an exponential r.v. with parameter ?=1/10. This professor only sees students in the office hour one at a time. Thus, if you arrive to the office and there is someone inside, you have to wait. Consider 5 randomly chosen days in which you visit the professor's office during the office hour period and someone arrives immediately ahead of you. What is the probability that in one of those days you will have to wait between 10 and 20 minutes?
Q. 3 A service time (in minutes) of post office is exponentially distributed with 2 = 0.2. (a) Suppose that no one is there, and that you get the service immediately. Find the probability that it takes more than 5 minutes to complete the business. (b) Suppose that someone else is in service ahead of you, and that you are next in line. Find the probability that you wait more than 5 minutes.
The probability that a vehicle will enter an intersection within a period of x minutes is given by P(x) = 1 -e-0.1x Determine symbolically the elapsed time x when there is a 50-50 chance that the vehicle has entered the intersection. The elapsed time is approximately min. (Type an integer or decimal rounded to two decimal places as needed.)
The lifetime, t, in hours, of an alkaline battery is exponentially distributed with ? = 0.10 per hour. What is the probability that the battery will last more than 18 hours?
A home fire alarm is believed to have a working life T in years given by hazard function Lamda(t) = .5 + 2t + t?. What is the probability it will still be working in 6 months? O .174 .389 O.493 O .571 O.582
6. The magnitude (Richter scale) of earthquake along a Taiwanese fault is exponentially distributed, with A= (1/2.5). What is the probability of an earthquake exceeding magnitude 6.4? There is 1 earthquake per year (on average) along the fault with magnitude greater than 5.5. Given this, what is the probability of an earthquake during the year that exceeds magnitude 7.2?
The time it takes to get a seat at a restaurant is exponentially distributed.The value for the function of time to get a table is 4.8 minutes for x ≥ 0Find the probability that a customer will have to wait at most 44 minutes to sit down.
gn X Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.41 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) P(X = X) X 0 1 2 3 4 5 6 7 8 (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) X 0 1 2 3 4 5 6 7 Use the cumulative distribution function of X to calculate P(2 ≤ x ≤ 5). (Round your answer to four decimal places.) P(2 ≤ x ≤ 5) = Need Help? Read It Watch It 4
Gabrielle has purchased the 2-year extended warranty from a retailer to cover the value of hers new cellphone in case if it gets damaged or becomes inoperable for the price of $25. Gabrielle's cellphone is worth $1400 and the probability that it gets damaged or becomes inoperable during the length of the extended warranty is estimated to be 4%. Let XX be the retailer's profit from selling the extended warranty. Answer the following questions: 1. Create the probability distribution table for XX : XX outcome profit xx ,$ P(X=x)P(X=x) the cellphone gets damaged or becomes inoperable no claim filed 2. Use the probability distribution table to find the following: E[X]=μX=E[X]=μX= dollars. (Round the answer to 1 decimal place.) SD[X]=σX=SD[X]=σX= dollars. (Round the answer to 1 decimal place.)
Exponential Distribution has a memoryless property. Intuitively, it means that the probability of customer service answering you call (assuming waiting time is exponential) in the next 10 mins is the same, no matter if you have waited an hour on the line or just picked up the phone. Formally, if X ∼ exponential(λ), f(x) = λ exp(-λx), and t and s are two positive numbers, use the definition of conditional probability to show that P(X > t + s | X > t) = P(X > s). Hint: Find the cdf of X first, and note that P(X > t + s Ç X > t) = P(X > t + s)