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

Is It Cheaper To Buy Auto Insurance Online?
Surprising as it may seem, the Progressive agent in your town does not necessarily sell the same insurance as the company on the Internet or on TV. This is true of several companies who advertise heavily on TV. The local agents in your town are usually independent agents who sell insurance...

Cost of living in Laramie, Wyoming versus Edinburgh, Scotland?
I've been in Edinburgh for the past 5 years and moved from Northern Colorado, so I can definitely give you advice on this.Edinburgh is far more expensive to live in than Laramie, especially due to the exchange rate, and finding work as a foreigner is quite difficult, especially with a foreign...

Where can I find a trustworthy extended warranty company for my car?
If you're looking for a warranty company that doesn't have horrible reviews, you'll be looking forever. Warranty companies are less popular than insurance companies - and insurance companies are not very popular.On a 7 year old vehicle, you won't find a 'reputable' warranty provider. Regular...

I need parts for a 89 4-door xj6 Jaguar. I live in the metro Detroit area.?
1988Lid/GateJaguar XJ 6 *XJ6-BLACK-4DR, 8371 $300.03 Mitch's Auto USA-MI(Detroit) Request_Quote 1-800-283-3634 Request_Insurance_Quote1991Lid/GateJaguar XJ 6 *XJ6-BLACK-SOVEREIGN 9921 $300.03 Mitch's Auto USA-MI(Detroit) Request_Quote 1-800-283-3634 Request_Insurance_Quote1992Lid/GateJaguar...

Are there insurance company equivalents of credit unions?
They are called mutuals, or mutual insurance companies. However, they are not necessarily cheaper. Moreover, there is a trend of converting mutual insurance companies into stock insurance companies.The largest mutuals in life and health lines are:New York Life InsuranceTIAA-CREFMass. Mutual...