1.State the binomial Distribution and its properties
2,Under what conditions and how would you use the binomial Approximation to poisson
A random sample of 6IC's is taken from a large consignment and tested in two independent
stages. The probability that an IC will pass either stage is p.All the 6IC's are tested at the first stage.
If 5 or more pass the test, those which pass are tested at the second stage.The consignment is accepted if
there is at most one failure at each stage.
What is the probability that the second stage of the test will not be required?
Find the number of IC's expected to undergo the second stage?

You can do 1. and 2. using google or consulting a textbook.

3. Let X be the random variable number of IC's that pass the stage 1 test.

X ~ Binomial(n = 6, p).

(a) Pr(X < 5) = .....

(b) Let Y be the random variable number of IC's that undergo the second stage test.

Note that Y = 0, 5 or 6.

E(Y) = (0) Pr(Y = 0) + (5) Pr(Y = 5) + (6) Pr(Y = 6) = (0) Pr(X < 5) + (5) Pr(X = 5) + (6) Pr(X = 6) = .....

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