Www.making-statistics-vital.co.uk MSV 11: Binomial Reverse.

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www.making-statistics-vital.co.uk MSV 11: Binomial Reverse

What is the most likely value for X? Question 1: X ~ B(11, 0.7). What is the most likely value for X? What happens if we turn this question around? Question 2: X ~ B(11, p) and 8 is the most likely value for X. What range of values can p take?

Binomial Reverse: Answers Question 1. The mean of the distribution is 7.7, so the only candidates for most likely value are 7 and 8. (The fact that 7.7 is nearer to 8 than 7 does not automatically guarantee that 8 is going to be the answer.) 11C7(0.7)7(0.3)4 = 0.220 11C8(0.7)8(0.3)3 = 0.257 So 8 is the most likely value.

11C7p7q4 = 11C8p8q3 , Question 2. The two boundary situations are: Taking the left-hand picture, we need to solve: 11C7p7q4 = 11C8p8q3 , which gives 330q = 165p.

11C8p8q3 = 11C9p9q2 , Taking the right-hand picture, we need to solve: which gives 165q = 55p.

is written by Jonny Griffiths www.making-statistics-vital.co.uk is written by Jonny Griffiths hello@jonny-griffiths.net