He horn of an auto operates on demand 99% of the time. Assume each time you hit the horn, it works or fails in?

He horn of an auto operates on demand 99% of the time. Assume each time you hit the horn, it works or fails in?

The horn of an auto operates on demand 99% of the time. Assume each time you hit the horn, it works or fails independently of all other times.(a) How many times do you expect to be able to honk the horn with 75% probability of not having any failures.(b) What is the expected number of times you hit the horn before the tenth failure?


Show that if T has the Weibull (¦E, ¦A) distribution with the following density: f (t) = ¦E¦At¦A1 e¦Et¦A(t > 0),where ¦E > 0 and ¦A > 0 then T ¦A has an exponential ¦E distribution. [b (10 points)]. Show that if U is uniform (0, 1) random variable then T = (¦E1 log U )1/¦A has a Weibull (¦E, ¦A) distribution. 3. Let Y be the minimum of 4 independent random variableswith uniform distribution on (0, 1) and let Z be their maximum. Find: [a (10 points)]. P (Z?U 3/4|Y ?Y 1/4). [b (10 points)]. P (Z ?U 3/4|Y?U 1/4). 4. Insurance claims arrive at an insurance company according to a Poisson process with rate ¦E. The amount of each claim has an exponential distribution with rate independently of times and amounts of all other claims. Let Xt denote the accumulated total of claims between time 0 and time t. Find simple formulae for [a (3 points)]. E(Xt ). 2 [b (5 points)]. E(Xt ). [c (5 points)]. SD(Xt ). [d (7 points)]. Corr(Xt , XS ) fort < s. 5. Let X1 , X2 , X3 , X4 be independent random variables with distribution Exp(¦E). Let Xmin denote the minimum of the X??s andXmax denote the maximum. [a (10 points)]. For a a, Xmax < b). [b (10 points)]. What is the joint density of Xmin andXmax ? 6. Let X and Y be the scores of the midterm and nal exams. Suppose that E[X] = 60 and E[Y ] = 70 and that all scores are between 0 and 100. [a (8 points)]. How can you upper bound P [X ?U 40, Y ?Y 90]? Is your bound optimal? [b (8 points)]. Suppose that in addition you are also given that (X, Y ) is bivariate normal with ¦N = 0.9 and SD(X) = SD(Y ) = 10. Find E[X|Y ?Y 90] and bound usingMarkov inequality P [X ?U 40|Y ?Y 90]. [c (6 points)]. Use the previous bound to obtain anupper bound on P [X ?U 40, Y ?Y 90] when (X, Y ) is bivariate normal with ¦N = 0.9 and SD(X)= SD(Y ) = 10.



Popular Q&A

Are there any associations one can join that would then give you access to group health insurance?
i live in indiana- the AARP plan is only a supplemental plan or they offer a hospital plan that from i read is basically a supplemental plan also-my husband has parkinsons disease and uninsurable in the state of indiana- i am healthy and filled out a individual application and was surprised...

In Ontario, how does auto insurance work? Do you need to insure yourself as a driver and your car separately?
Yes you insure the car and yourself as the driver and then can add drivers and more coverage to the policy if you want to.Basically you must get a standard coverage such as 1 million dollar liability or basic coverage if driving it.Hope that helps and best of luck.By the way shop around for...

How can I pull my own CLUE insurance report?
Similar to your credit report, you are entitled to view your CLUE report once per year at no charge. I've done it, just can't remember the URL. Google it.

What are some discounts that many auto insurance companies offer that might help save some money?
Depends on the company and the state that you live in. Auto insurance is regulated by each state so it can differ from state to state.Some companies might offer:-Good student discount (if you have a B or better average, so 3.0 or higher)-Driver Training discount (if you got your drivers license...

How much more would insurance rates be if I had a convertible?
theres are more factors in price than just the car you drive. if you are needing to carry full coverage, its going to break your bank at 16. if you only need liability, it won't matter the car you drive. liability rates should stay the same for any car you have. liability covers other autos...