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Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: Bi Bernoulli(p) for i = 1, 2, 3, ..., n. Question part 2: Derive the MGF of X = B1 + B2+..+Bn = E=1 Bi vi=1 Hint: recall that for independent random variables X and Y and functions f() and g(), E[f(X)q{Y)] = E[r(x)] E[oC)] %3D O п(1 — р+ pe") enpt О (1 -р+pе')п O n(e (1 — р) + р)

Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: Bi Bernoulli(p) for i = 1, 2, 3, ..., n. Question part 2: Derive the MGF of X = B1 + B2+..+Bn = E=1 Bi vi=1 Hint: recall that for independent random variables X and Y and functions f() and g(), E[f(X)q{Y)] = E[r(x)] E[oC)] %3D O п(1 — р+ pe") enpt О (1 -р+pе')п O n(e (1 — р) + р)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: B; Bernoulli(p) for i = 1, 2, 3, ..., n. Question part 2: Derive the MGF of X = B1 + B2+...+Bn = D"1 B¡ Hint: recall that for independent random variables X and Y and functions f() and g(), E E O n(1 – p+ pe*) enpt о (1-р+pе')" O n(e*(1 – p) + p)
Transcribed Image Text:Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: B; Bernoulli(p) for i = 1, 2, 3, ..., n. Question part 2: Derive the MGF of X = B1 + B2+...+Bn = D"1 B¡ Hint: recall that for independent random variables X and Y and functions f() and g(), E E O n(1 – p+ pe*) enpt о (1-р+pе')" O n(e*(1 – p) + p)
Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: B; Bernoulli(p) for i = 1, 2, 3, ..., n. Question part 1: Derive the mgf of any one of the B; (since they are i.i.d., each one has the same mgf) et +1 01-p+ pe* O e' (1 – p) + p O etp
Transcribed Image Text:Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: B; Bernoulli(p) for i = 1, 2, 3, ..., n. Question part 1: Derive the mgf of any one of the B; (since they are i.i.d., each one has the same mgf) et +1 01-p+ pe* O e' (1 – p) + p O etp
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