I have coursework that's due on monday, most of which I can easily solve. However, this short question is beyond my understanding. It's probably easy as pi, but I can't get my head around it:
The number of breakdowns per week for a type of computer is a random variable Y having a Poisson distribution with mean mu. A random sample Y1, Y2... Yn of observations on the weekly number of breakdowns is available. The weekly cost of reparing the breakdowns is C = 3Y + Y^2. Show that E[C] = 4mu + mu^2. Also find a function of Y1, Y2... Yn that is an unbiased estimator for E[C].
OK, we have that the unbiased estimator of Y is E[Ybar], right? So what? I know how to deal with variables of form M = aX + b, but nothing above the linear case.
Some educated help please?
None.
Here's your answer:
"The poisson distribution is an unfair explanation of things that happen naturally, and is rather sacrilegious. Who are we to assign numerical probabilities to things that are left in God's hands?"
I've wanted to put that answer down since I took probability in high school. And when I got to bus stats in college, I wussed out.
I needed it to graduate. Sorry for wasting your time.
Oh it's allright, don't worry. Probability says that most of the replies in this topic won't be constructive, since SEN isn't exactly a math forum.
None.
Honest, if I hadn't sold that textbook back to the bookstore you'd probably have my help.
I'm not that good with Poisson Distribution, but this might help:
If random Variable Y has a Poisson distribution with parameter λ, then E(Y) = V(Y) = λ. With the limits being np -> λ and np(1-p) -> λ
None.
If random Variable Y has a Poisson distribution with parameter λ, then E(Y) = V(Y) = λ. With the limits being np -> λ and np(1-p) -> λ
Yes, assuming the right conditions it is close to the binomial distribution?.. Also, by the CLT, assuming sample is big enough, we can use Ybar ~~ N(mu, mu/n), right?
...so what does that give me? >_< Sorry if I don't see what you're trying to tell me - it's almost 12 in the evening here, so be a bit less subtle please.
None.
If random Variable Y has a Poisson distribution with parameter λ, then E(Y) = V(Y) = λ. With the limits being np -> λ and np(1-p) -> λ
Yes, assuming the right conditions it is close to the binomial distribution?.. Also, by the CLT, assuming sample is big enough, we can use Ybar ~~ N(mu, mu/n), right?
"For large n and small p, with np = λ, the binomial distribution Bi(n,p) approximates to Po(λ)," says the Collins dictionary of Mathematics.
Post has been edited 1 time(s), last time on Mar 9 2009, 12:10 am by A_of-s_t.
Yeah, that's what I said, which does not bring me closer to the truth.
...and my time is running out. Soon, the tide of total sleepiness shall conquer my mind.
None.
