Hello everyone, I can't solve 2 problem during 4 hours....

Suppose that a tray of eggs consists 10 egg and there are 10 trays(i.e. there is 100 eggs). If a person take 15 eggs from 100 eggs at random, what is the expected number of trays that remain intact?

-> Do I have to use some special Distribution? Like binomial or,,

Three coins are tossed n times (Assume that each coin is indentical)
(a) Find the joint density of X, the number of times no heads appear; Y, the number of times one head appears; and Z, the number of times two heads appear.
(b) Find the conditional mass function of X and Z given Y.

I know the meaning of joint density, but how can i get it?

1. It seems that the best approach will be using the indicator (Bernoulli random variable). Let be the indicator of the -th tray remain intact. Then the number of trays remain intact is the sum of them and you can proceed.

2. Technically speaking you are finding the joint probability mass function as they are discrete. And this is just the multinomial distribution (try to think of the reason).

[QUOTE=BGM;168073]1. It seems that the best approach will be using the indicator (Bernoulli random variable). Let be the indicator of the -th tray remain intact. Then the number of trays remain intact is the sum of them and you can proceed.

Thank you, I solve 2nd problem. And first one, In that case, are iid? If they aren't, How Can I get expectation by sum of them?

Yes this is the "tricky" part (although not really tricky). Those indicators are not independent - but it does not matter as you are only calculation the expectation of a sum. The linearity of expectation stills hold even the summand are dependent.