Math Is Fun Forum

Say for example,
you had $100 in your bank accout 1 year ago
and the bank pays you 4% interest
now you have $104 in your account
you can say that you have 104% of the original amount you put in your bank 1 year ago

the distribution you stated is called Cauchy distribution.
Wikipedia has a very good explanation for why the mean is undefined.

http://en.wikipedia.org/wiki/Cauchy_distribution

Read the section "Explanation of undefined moments"

Cheers

the answer is 32/3
What is your F(x)?

It should be x^3 + x

Cheers

I have a feeling that we may be able to solve this without enumerating all the combination

Let y_max be the point of the largest of the six card
Let y be the point of a card drawn randomly from the deck

we can work out the probability mass function of y_max

say for example,

P(y_max = 10) = 6!/5! P(y = 10) (P(y <= 10 | a card with 10 points is drawn))^5
= 6*P(y = 10)

we can then work out the probability mass function of y_(5), which is the poit of the second largest card.

Haven't think about it carefully. But i think we might tackle this problem using the idea similar to order statistics.

You can imagine a simpler scenario.
There are 10 balls in an urn. 5 are red and 5 are white.

You get 1 point when you get a red and get 0 when you get a white.
You now draw two balls from the urn. What is the expected points that you will get?

Cheers

You can now try to work out the last step. (Bear in mind that X follows an exponential distribution)

Cheers

you can do a first step analysis for this question.
P(A gets n heads before B gets m heads)
= P(A gets n before B gets m | first toss is head)P(first toss is head) + P(A gets n before B gets m | first toss is tail)P(first toss is tail)

Cheers