Consider the Moment Generating Function (MGF) of the Binomial distribution Mx(t) = ((1 − p) + pet)n (p is the probability of success and n is the number of trials). Using the MGF derive E[X] and Var[X].

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Consider the Moment Generating Function (MGF) of the Binomial distribution Mx (t)
((1 − p) + pet)n (p is the probability of success and n is the number of trials). Using
the MGF derive E[X] and Var[X].
=
Consider random independent variables X₁, X₂, ... Xn which take 0 with the probability
1 − p and 1 with the probability p.
(a) Derive an expression for EXj
[X]
(b) Find the Fisher's information I (p)
Transcribed Image Text:Consider the Moment Generating Function (MGF) of the Binomial distribution Mx (t) ((1 − p) + pet)n (p is the probability of success and n is the number of trials). Using the MGF derive E[X] and Var[X]. = Consider random independent variables X₁, X₂, ... Xn which take 0 with the probability 1 − p and 1 with the probability p. (a) Derive an expression for EXj [X] (b) Find the Fisher's information I (p)
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