charleneyin
New Member
- Joined
- May 10, 2010
- Messages
- 17
- Gender
- Undisclosed
- HSC
- 2009
Q1 A hen lays N eggs, where N has the Poisson distribution with parameter . Each
egg hatches with probability p independently of the other eggs. Let K be the number
of chicks. What is the conditional expectation of the initial number N of eggs, given
that we observe k chicks? What is Var(N/K = k)?
Q2 We roll a die n times. Let Aij be the event that the ith and jth rolls produce the same
number. Show that the events {Aij ; 1 <= i < j <=n} are pairwise independent but not
jointly independent.
egg hatches with probability p independently of the other eggs. Let K be the number
of chicks. What is the conditional expectation of the initial number N of eggs, given
that we observe k chicks? What is Var(N/K = k)?
Q2 We roll a die n times. Let Aij be the event that the ith and jth rolls produce the same
number. Show that the events {Aij ; 1 <= i < j <=n} are pairwise independent but not
jointly independent.
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