Question
Download Solution PDFIn a binomial distribution, the mean is 4 and variance is 3. Then its mode is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFIn Binomial distribution, Mean = np, Variance = npq and the mode is r if for x = r, the probability function p(x) is maximum.
Given np = 4 and npq = 3
\(\therefore {\rm{q\;}} = {\rm{\;}}\frac{3}{4}{\rm{\;and\;p\;}} = {\rm{\;}}1 - {\rm{q\;}} = {\rm{\;}}1 - \frac{3}{4}{\rm{\;}} = {\rm{\;}}\frac{1}{4}\)
Also, \({\rm{n\;}} = {\rm{\;}}\frac{4}{{\rm{p}}}{\rm{\;}} = {\rm{\;}}\frac{4}{{\frac{1}{4}}}{\rm{\;}} = {\rm{\;}}16\)
Now, \(\left( {{\rm{n}} + 1} \right){\rm{p\;}} = {\rm{\;}}\left( {16 + 1} \right)\frac{1}{4}{\rm{\;}} = {\rm{\;}}\frac{{17}}{4}{\rm{\;}} = {\rm{\;}}4 + \frac{1}{4}\)Last updated on Jun 26, 2025
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