I am new to Statistics and R. So, I'm stumbling upon certain problems. Please bear with me.
There' a question - 2% items in a factory are defective. What is the probability that there will be 2 defective items in 100 items?
My textbook solved it as a Poisson distribution and took l = np = 2.
Then it solved using PDF to get the answer as 0.2706.
The corresponding R syntax is
I solved using binomial distribution and used
dbinom(2, 100, 0.02) but got something different. However
dbinom(1, 100, 0.02) comes near to the Poisson distribution answer.
So, I learnt that Poisson is a special kind of Binomial where n tends to infinity and p is very small. But however they should give same results, shouldn't they?
Maybe I'm asking something very trivial and missing something. Please help me out. Thanks in advance.