Question

suppose that X ~ Bin(n, p) a. show that E(X^k)=npE((Y+1)^(k-1)) where Y ~ Bin(n-1, p) b....

suppose that X ~ Bin(n, p)

a. show that E(X^k)=npE((Y+1)^(k-1)) where Y ~ Bin(n-1, p)

b. use part (a) to find E(x^2)

Math   Statistics-And-Probability   
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Answer #1

where Y ~ B(n-1 , p)

So using this , E (X2) = np E( Y+1)

  

  

So,

   ( because sum of probability of all values of random variable =1)

Mean of a random variable ~ B(n,p)  = E(X) = np

this implies

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