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Suchithra’s Statistics Classes
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Binomial Distribution – B.D
Part – 4
(Based on complementary Statistics
of Bsc , University of Calicut)
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
P(X=x) = f(x) = nCx px qn-x
Moment generating function --- m.g.f
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Additive property of B. D
This can be extend to any number of independent r.vs if p is same.
If the p is not the same then X+Y will not be binomial.
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Characteristic function of B.D
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Mode of a probability distribution is the value of the r.v
having maximum probability.
If x is the mode of a distribution, f(x) will be the maximum
This can be split into
Mode of B.D
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
On simplification we get
Therefore the mode corresponds to the values of x which lies
between
Combing (1) & (2)
If (n+1) p is an integer say k , then the mode is at X=k & X=k-1 ,i.e;
the B.D is bimodal.
If (n+1)p is not an integer, then integer part of (n+1)p is the mode of
the B.D (Uni model).
Things to be clear from this class
• How to find m.g.f of a B.D ? Hence deduce
central moments.
• Additive property of B.D.
• How to find the Characteristic function of a
B.D.
• Calculate & interpret Mode of a B.D.
Suchithra's Statistics Classes -- Binomial Distribution, Part 4
Thank you for watching,
if this is found to be useful then
like & subscribe.
Suchithra’s Statistics classes
Suchithra's Statistics Classes -- Binomial Distribution, Part 4

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Binomial Distribution Part 4

  • 1. Welcome Suchithra’s Statistics Classes Suchithra's Statistics Classes -- Binomial Distribution, Part 4
  • 2. Binomial Distribution – B.D Part – 4 (Based on complementary Statistics of Bsc , University of Calicut) Suchithra's Statistics Classes -- Binomial Distribution, Part 4
  • 3. Suchithra's Statistics Classes -- Binomial Distribution, Part 4 P(X=x) = f(x) = nCx px qn-x Moment generating function --- m.g.f
  • 4. Suchithra's Statistics Classes -- Binomial Distribution, Part 4
  • 5. Suchithra's Statistics Classes -- Binomial Distribution, Part 4
  • 6. Suchithra's Statistics Classes -- Binomial Distribution, Part 4
  • 7. Suchithra's Statistics Classes -- Binomial Distribution, Part 4 Additive property of B. D This can be extend to any number of independent r.vs if p is same. If the p is not the same then X+Y will not be binomial.
  • 8. Suchithra's Statistics Classes -- Binomial Distribution, Part 4 Characteristic function of B.D
  • 9. Suchithra's Statistics Classes -- Binomial Distribution, Part 4 Mode of a probability distribution is the value of the r.v having maximum probability. If x is the mode of a distribution, f(x) will be the maximum This can be split into Mode of B.D
  • 10. Suchithra's Statistics Classes -- Binomial Distribution, Part 4
  • 11. Suchithra's Statistics Classes -- Binomial Distribution, Part 4 On simplification we get Therefore the mode corresponds to the values of x which lies between Combing (1) & (2) If (n+1) p is an integer say k , then the mode is at X=k & X=k-1 ,i.e; the B.D is bimodal. If (n+1)p is not an integer, then integer part of (n+1)p is the mode of the B.D (Uni model).
  • 12. Things to be clear from this class • How to find m.g.f of a B.D ? Hence deduce central moments. • Additive property of B.D. • How to find the Characteristic function of a B.D. • Calculate & interpret Mode of a B.D. Suchithra's Statistics Classes -- Binomial Distribution, Part 4
  • 13. Thank you for watching, if this is found to be useful then like & subscribe. Suchithra’s Statistics classes Suchithra's Statistics Classes -- Binomial Distribution, Part 4