8.18. Let X be a binomial random variable with parameters n and p, which meansthat its mass function is given byƒ(1) = (*)p'′(1—p)*-', i=0,...,n,and 0 otherwise. Prove that810=(1+x)= 1-(1-p)"+1(n+1)p

X~B(n,p)Probability mass functionf(i)=n i pi(1-p)n-i. i =0,1,2,...n Formula Used for expected…

Answered: 8.18. Let X be a binomial random…

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8.18. Let X be a binomial random variable with parameters n and p, which means that its mass function is given by ƒ(1 (*)p²(1–p)**, = (*) p² (1-p)*-*, i=0,...,, and 0 otherwise. Prove that E 1+X = 1-(1-p)"+1 (n+1)p
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8.18. Let X be a binomial random variable with parameters n and p, which means that its mass function is given by ƒ(1)= (*)p'(1-p)*-', i=0,...,”7, and 0 otherwise. Prove that 810 = [1 + x) = 1 = (1-P) ²+1 (n+1)p

8.18. Let X be a binomial random variable with parameters n and p, which means that its mass function is given by ƒ(1)= ()p'(1-p)-', i=0,...,”7, and 0 otherwise. Prove that 810 = [1 + x) = 1 = (1-P) ²+1 (n+1)p