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A grade statisticians. Solved problem

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If X ,X ,...,X are independent random variables having Bernoulli distributions with the parameter θ,then is the proportion of successes in n trials, which we denote by . Verify that (a) E( ) ; ... ( ) X b     µ  1  var( ) = . n    Answer:       Let X ,X ,...,X be an independent random v 1 2 n ariables having identical having Bernoulli distributions with the parameter θ. Then E X nθ and var X =nθ 1-θ .  Let X be the proportion of successes in n trials, which is denoted by Θµ . µ X That is Θ n  µ     X a)EΘ E n 1 = E X n 1 = nθ=θ n          _____________________________________________________________________________ _____________________________________________________________________________ __ This study source was downloaded by 100000823742721 from CourseHero.com on 07-31-2021 14:46:20 GMT -05:00 https://www.coursehero.com/file/12508945/problem-2/ Th [Show More]

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