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Binomial Distribution deepthi.pptxpptx12
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- 2. CONTENTS Introduction Whatis binomial distribution? Formula of binomial distribution Problem Applications of binomial distribution
- 3. INTRODUCTION Binomial distributionwas discovered by JAMES BERNOILLI in 1738. This is a discrete probability distribution. Binomial Distribution in Probability can be implemented when there are two possible outcomes i.e. Success or Failure
- 4. What is binomialdistribution? A random variable X has a binomial distribution it assumes only non-negative values and its probability density function is given by p(r)={n Cr pr qn-r r=0,1,2,3…..n 0 q=1-p otherwise p+q=1
- 5. Formulas of binomialdistributions Mean of binomial distribution: mean( μ) = np Variance of binomial distributions: variance σ2 = npq Standard Deviation of binomial distributions: standard deviation σ= √(npq) Where p is the probability of success q is the probability of failure, where q = 1-p
- 6. Q: 8coins are tossed . Find the probability of getting heads p(x=3) Solution: Given that n=8 p=1/2,q=1/2 p(r)= n Cr pr qn-r = 8 C3 (1/2)3 (1/2)8-3 = 8 C3 (1/2)3 (1/2)5 = 8 C3 (1/8)(1/32) = 56(1/8)(1/32) =7/32=0.21875
- 7. Applications ofbinomial distribution : There are a fixed number of trials or experiments. Each trial has two possible outcomes (success or failure). The probability of success is constant across trials. The trials are independent of one another.
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