STATISTICS-I PRACTICAL PROBLEMS BINOMIAL DISTRIBUTION 1) Fit a Binomial Distribution for the following data. X 0 1 2 3 4 5 6 7 f 0 4 13 28 42 20 6 2 Solution : - Aim : - P(X=x) = n c x p x q n-x ; dž=Ϭ,ϭ,Ϯ,…. ; p+Ƌ=ϭ = 0 ; otherwise Where n,p are parameters of the distribution. Mean =   = np => ࢖  =  ࢔  => ࢗ =1-࢖  Where   = ࢌ࢞ ࢌ Calculations:- First we have to calculate about mean Here n=7 Mean =  = ࢌ࢞ ࢌ = ૝૜૛ ૚૚૞ = 3.756 But ࢖  =  ࢔  = ૜.ૠ૞૟ ૠ = 0.536  ࢗ =1-࢖  = 1-0.536=0.464 X f fx 0 0 0 1 4 4 2 13 26 3 28 84 4 42 168 5 20 100 6 6 36 7 2 14 115 432 X f Probability P(X=x) = n c x p x q n-x Expected Frequency = N. P(X=x) 0 0 0.004630 0.532≅1 1 4 0.037443 4.305≈4 2 13 0.129759 14.922≅15 3 28 0.249824 28.729≅29 4 42 0.288589 33.187≅33 5 20 0.200022 23.002≅23 6 6 0.77020 8.857≅9 7 2 0.012710 1.461≅1 115 115