Let the (discrete) random variable X be the result of a single roll of a standar

Question

Let the (discrete) random variable X be the result of a single roll of a standard six-sided die with probability distribution d(x) = P(X = x) given by: d(1) = 0.1, d(2) = 0.2, d(3) = 0.3, d(4) = 0.15, d(5) = 0.1.

Same Situation: Consider the experiment of rolling 10 dice of the type described above, and let Y be the number of 5's rolled.

Y is a binomial random variable with Y~Bin(10,p). (You will need to have calculated p.)

Why is a Poisson Distribution not an appropriate approximation to the binomial distribution of Y?

A.The Poisson Distribution is never a good approximation to a Binomial Distribution.

C. n is too small

D. np is too large

Explanation / Answer

The Poisson distribution not an appropriate approximation to Binomial distribution in this scenario is with increase in number of n, p tends to 0, and np becomes too small. Option B.

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