Proabability question

A bag has 4 counters. 2 are worth £2, 1 is worth £4 and 1 is worth £8.
(a) You randomly select a counter, gaining £X. Find E(X) and Var(X)
(b) You place the first counter in your pocket. You then draw a second
counter from the bag at random. This counter has value £Y . Without further calculations,
write down Exp(y) and var(y)

I am not quite sure how to do b, would you have to consider each case seperatly??

Reply 1

ghostwalker

17

Original post by number23

I am not quite sure how to do b, would you have to consider each case seperatly??

No, no calculation is required.

This may help.

Imagine you just take a first counter out of the bag, and without looking at it put it in your pocket.

Then take the second counter. What's the expectation/variance of this second selection.

I can think of one more scenario that might give a clue, if you're still stuck.

Reply 2

number23

OP

15

Original post by ghostwalker

No, no calculation is required.

This may help.

Imagine you just take a first counter out of the bag, and without looking at it put it in your pocket.

Then take the second counter. What's the expectation/variance of this second selection.

I can think of one more scenario that might give a clue, if you're still stuck.

I think the expectation and variance are the same but not sure exactly why, what was ur other example? :smile:

Reply 3

ghostwalker

17

Original post by number23

I think the expectation and variance are the same but not sure exactly why, what was ur other example? :smile:

Yes they are.

Put your hand in the bag, pick a coin, but don't pull it out. Let it go, and pick a different coin and pull that one out.

Reply 4

metaltron

11

Original post by number23

I think the expectation and variance are the same but not sure exactly why, what was ur other example? :smile:

If you are expected to pick a £4 counter, and there is a £4 counter in the bag, what would be the effect if you took it out?

Proabability question

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