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Exercises. Central limit theorem. Exercises. The binomial distribution converges against the normal distribution since it is a sum of independent and identically distributed random variables, X~Bin ( n,p ) and : -> N(0,1 ). Exercises.

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exercises

Exercises

Central limittheorem

exercises1
Exercises
  • The binomialdistributionconvergesagainstthe normal distributionsinceitis a sumofindependentandidenticallydistributedrandom variables, X~Bin(n,p) and: -> N(0,1)
exercises2
Exercises
  • whereand for Bernoulli-variables. (Binomial: and )
exercises3
Exercises
  • Exercise: n=120, p=0.515, X~Bin(n,p), binomialdistribution
  • Compute P(X >=70)!
exercises4
Exercises
  • Exercise: n=120, p=0.515, X~Bin(n,p), binomialdistribution
  • Compute P(X >=70)!
  • witch Z~N(0,1)

asymptotic N(0,1)

distributedaccordingtocentrallimittheorem