Question

In: Statistics and Probability

​From a lot containing 25 items, 5 of which are defective, 4 are chosen at random. Let Y be the number of defectives found. Obtain the probability distribution of Y if


From a lot containing 25 items, 5 of which are defective, 4 are chosen at random. Let Y be the number of defectives found. Obtain the probability distribution of Y if

 (a) the items are chosen with replacement,

 (b) the items are chosen without replacement.

Solutions

Expert Solution

a)

here as experiment is done with replacement ; composition of sample remains same therefore events are independent

probability distribution of Y is binomial with parameter n=4 and p=5/25=1/5

b)

as events are not independent; this is hypergeometric distribution:

with parameter N=25 , n=4 and k=5

orchestra answered 1 year ago
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