# Thread: Statistic and it's sampling distribution

1. ## Statistic and it's sampling distribution

A large bag of counters has 25% with the number 0 on, 25% with the number 2 on, and 50% with the number 1. A random sample of size 3 is taken from the bag.
(a) List all the possible samples
(b) Find the sampling distribution for median N.

For (a) it will be (000),(001),(010),(100),(002),(020),(200),(111),(1 10),(101),(011),(222),
(220),(202),(022),(112),(121),(211),(221),(212),(1 22),(012),(102),(201),(021),(120),(210)

For (b) how to find the solution? I’m getting the wrong distribution.

N 0 1 2
P(n) 10/64 44/64 10/64

ie P(n=0)=10/64
P(n=1) = 44/64
P(n=2) = 10/64

Pls help me on (b). What are the samples come for P(n=0)?

2. Originally Posted by Sashikala
A large bag of counters has 25% with the number 0 on, 25% with the number 2 on, and 50% with the number 1. A random sample of size 3 is taken from the bag.
(a) List all the possible samples
(b) Find the sampling distribution for median N.

For (a) it will be (000),(001),(010),(100),(002),(020),(200),(111),(1 10),(101),(011),(222),
(220),(202),(022),(112),(121),(211),(221),(212),(1 22),(012),(102),(201),(021),(120),(210)

For (b) how to find the solution? I’m getting the wrong distribution.

N 0 1 2
P(n) 10/64 44/64 10/64

ie P(n=0)=10/64
P(n=1) = 44/64
P(n=2) = 10/64

Pls help me on (b). What are the samples come for P(n=0)?
You need to note that the events in the sampling distribution are not all equally likely ....

3. ## Statistic and it's sampling distribution

Still I am unable to find the distribution for (b).

4. Originally Posted by Sashikala
Still I am unable to find the distribution for (b).
What events give a median of 0? Calculate the probability of those events occuring.

What events give a median of 1? Calculate the probability of those events occuring.

What events give a median of 2? Calculate the probability of those events occuring.

Note that the events are not all equally likely so you need to take care calculating the probabilities.

5. ## Statistic and it's sampling distribution

I guess I have to figure it the following way.
Events give median 0 will be
(000),(001),(010),(100),(002),(020),(200) č hence the respective probability will be:
(1/4)3+3*(1/4)2*(1/2)+3*(1/4)2*(1/4)=1+6+3 =10/64
64
same way I need to do for median 1 and median 2.
Thanks very much.