# Question

Use the recursion formula of Exercise 5.8 to show that for θ = 12 the binomial distribution has

(a) A maximum at x = n/2 when n is even;

(b) Maxima at x = n – 1 / 2 and x = n + 1 / 2 when n is odd.

In exercise

(a) A maximum at x = n/2 when n is even;

(b) Maxima at x = n – 1 / 2 and x = n + 1 / 2 when n is odd.

In exercise

## Answer to relevant Questions

Suppose the acceptance number in Example 5.16 is changed from 1 to 2. Keeping the producer’s risk at 0.05 and the consumer’s risk at 0.10, what are the new values of the AQL and the LTPD? Find the AQL and the LTPD of the sampling plan in Exercise 5.93 if both the producer’s and consumer’s risks are 0.10. Show that if a random variable has an exponential density with the parameter θ, the probability that it will take on a value less than – θ ∙ ln(1 – ρ) is equal to p for 0 ≥ p < 1. Show that if α > 1 and β > 1, the beta density has a relative maximum at If X is a random variable having a normal distribution with the mean µ and the standard deviation s, use the third part of Theorem 4.10 on page 128 and Theorem 6.6 to show that the moment– generating function of Z = X ...Post your question

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