Problem 783

[spidersanghvi]

So I do not know if asking this is fine but when I am calculating the value of E(2,2) I am getting the value 8.666667.Am I missing something?

[neverforget]

Please include the link to the problem in the first post, like this: Problem 783 (View Problem)

And to answer your question, you must be missing something because $E(2,2)$ is easy enough to verify by hand, and the stated value in the problem is definitely correct. I would suggest carefully rereading the problem statement, as that is usually where the problem lies when small examples don't match.

[PeterBurbery]

I am wondering if the a sequence of balls is removed all at once or a ball is removed one by one.

[RobertStanforth]

I am wondering if the a sequence of balls is removed all at once or a ball is removed one by one.

"On each turn [...] $2k$ random balls are removed from the urn"
These $2k$ are selected in such a way that any possible choice of $2k$ is as likely as any other.
It doesn't make any difference to the distribution of $B_t$ whether all $2k$ balls for turn $t$ are selected/removed at once, or one at a time.

[PeterBurbery]

I am wondering if this is a place where I can ask questions about Wolfram mathematica and functions.

[PeterBurbery]

I'm just wondering but what does the expectation of mean?
Further define E(n,k) as the expectation of

[jaap]

I'm just wondering but what does the expectation of mean?

Further define E(n,k) as the expectation of

It means the expected value.