FITTING OF BINOMIAL DISTRIBUTION

FITTING OF BINOMIAL DISTRIBUTION
RESEARCH METHODOLOGY

DR. SHASHI AGAGRWAL

PROCEDURE

THE FOLLOWING PROCEDURE IS ADOPTED WHILE FITTING A BIO NOMINAL DISTRIBUTION

1. DETERMINE THE VALUE OF p AND q FROM THE GIVEN INFORMATION
2. NOTE THE VALUE OF n  AND N WHERE n IS THE NUMBER OF TRIALS IN AN EXPERIMENT AND N IS THE TOTAL NUMBER OF TRIALS IN ALL THE EXPERIMENT,
3. FIND THE PROBABILITY OF ALL POSSIBLE NUMBER OF SUCCESS OUT OF GIVEN EXPERIMENT
4. MULTIPLY THESE PROBABILITIES BY THE N AND THE RESULT WILL THE REQUIRED EXPECTED FREQUENCY.

5.     QUESTION

SOLUTION

UNDER THE ASSUMPTION THAT COINS ARE UNBIASED.

THE PROBABILITY OF HEAD(p) AND THE PROBABILITY OF q ARE ½ AND ½

IN THIS CASE n=4 and N=160

THE PROBABILITY OF 0,1,2,3,4 HEADS WILL BE GIVEN BY

SOLUTION

HERE n=4

N=150

X MEAN=∑fx/N=200/150=4/3

np=MEAN=4/3=4p=4/3=4/12=p=1/3,q=1-1/3=2/3

P(X=x)=ⁿC_xq^n-x.p^x=Nx ⁿC_xq^n-x.p^x

 

  EXPECTED FREQUENCY=NX ⁿC_xq^n-x.p^x=Nx ⁿC_xq^n-x.p^x