anonymous
  • anonymous
Some of the eggs at a market are sold in boxes of six. The number, X, of broken eggs in a box has the probability distribution given in the following table. x 0 1 2 3 4 5 6 P(X=x) 0.8 0.14 0.03 0.02 0.01 0 0 (Find the expectation and variance of the number of unbroken eggs in a box)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
dape
  • dape
Have you started solving the problem?
anonymous
  • anonymous
I don't know the unbroken eggs. I know how to get the expectation and variance once I have the distribution of unbroken eggs..
dape
  • dape
Well, the expected value of unbroken eggs is just the difference of the total number of eggs and the expected value of broken eggs or \[ E(unbroken) = 6-E(broken) \]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
@dape what of the variance?
dape
  • dape
Calculate the deviations with the respect to the mean of the number of unbroken eggs instead of the mean of broken eggs.
anonymous
  • anonymous
How do you do that?
anonymous
  • anonymous
@dape
anonymous
  • anonymous
it is about discrete type random variable.
dape
  • dape
You use the expected value, I said mean but meant EV. Calculate the variance from the EV of the number of unbroken eggs.
dape
  • dape
Variance is calculated by summing the square of the distances of the possibilities from the mean or expectation and dividing by the number of possibilities.
anonymous
  • anonymous
Yes, so how do you do that with this probability distribution?
dape
  • dape
\[ Var[unbroken] = P[X=0]*(0-E[X=0])^2 + P[X=1]*(1-E[X=1]) ...\]
anonymous
  • anonymous
Can you place some values in that equation? I'm not sure what E[X=0] stands for?
dape
  • dape
Sorry, you're right, that doesn't make sense, it should be \[ Var = P[X=0]*(0-E[X])^2+P[X=1]*(1-E[X])^2+...+P[X=6]*(6-E[X])^2 \]
anonymous
  • anonymous
But what does E|X| stand for?
dape
  • dape
Expected value of the random variable.
anonymous
  • anonymous
Yea, but what would be the expectd value when X= 0 for instance? Or are they all just the expectation value?
dape
  • dape
Yes, they are all the expectation. My first formula doesn't really make sense.
anonymous
  • anonymous
So just 5.7? All of them?
dape
  • dape
Yes, you calculate how far they are from the average.
anonymous
  • anonymous
Ok. Thankyou! :)
dape
  • dape
Well, now it got confusing. It should be \[ P[X=0]*(6-E[X])^2 \] and not \[ P[X=0]*(0-E[X])^2 \] since the 0 is the number of broken eggs and we want to calculate the variance of unbroken eggs, so X=0 means 6 unbroken eggs and so on.
phi
  • phi
There might be another way to do this, but if you notice x 6 5 4 3 2 1 0 P(X=x) 0.8 0.14 0.03 0.02 0.01 0 0 is the probability distribution of whole eggs, you can make progress
phi
  • phi
E(whole)= 5.7 var(whole)= 0.51
phi
  • phi
Did I lose you?
phi
  • phi
0.8 probability of 0 eggs broken means 0.8 probability of 6 whole eggs....
anonymous
  • anonymous
It says the variance is 1.7? Yes, I'm lost.
dape
  • dape
I got calculated the variance to 0.51, which agrees with phi's calculation. Where does it say the variance is 1.7?

Looking for something else?

Not the answer you are looking for? Search for more explanations.