Sample Size determination and Variance of binomial Let X th

Sample Size determination and Variance of binomial.

Let X = the act of noting whether or not an o-ring will fracture at the sub-freezing temperature 30 degree F. \'Let the event that a fracture occurs be [X = 1]. and let Pr[X = 1] = p . Then X ~ Ber(p). It follows that mu_x = as a scaled binomial(n, p) random variable [i.e. it has the same lumps of probability as a binomial(n, p) random variable, but on the scaled sample space {0.1/ n.2 / n, Lmabda .(n -1)/ n,1} ]. Since sigma_x^2 = p - p^2, equation (1.1) gives Var(mu x) = (p-p^2)/n-However, p = mu x is the unknown here. Consequently, we don\'t know Var(mu x). Use differential calculus to prove that Var(mu x)

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