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Question part 1: Derive the mgf of any one of the B; (since they are i.i.d., each one has the same mgf)

Question part 1: Derive the mgf of any one of the B; (since they are i.i.d., each one has the same mgf)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 21E
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Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: B; "A Bernoulli(p) for i = 1,2, 3, ..., n. .. , 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) etp et +1 O e' (1 – p) + p 01-р+pеt
Transcribed Image Text:Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: B; "A Bernoulli(p) for i = 1,2, 3, ..., n. .. , 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) etp et +1 O e' (1 – p) + p 01-р+pеt
Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: B; Вernoulli(p) for i 3D 1,2, 3, ..., п. Question part 2: Derive the MGF of X = B1 + B2+...+Br = E÷1 B; n i=1 Hint: recall that for independent random variables X and Y and functions f() and g(), E = E E O n(e' (1 – p) + p) о (1-р+pе")" O n(1 – p+ pe*) enpt
Transcribed Image Text:Assume a series of n independent and identically distributed Bernoulli random i.i.d. variables: B; Вernoulli(p) for i 3D 1,2, 3, ..., п. Question part 2: Derive the MGF of X = B1 + B2+...+Br = E÷1 B; n i=1 Hint: recall that for independent random variables X and Y and functions f() and g(), E = E E O n(e' (1 – p) + p) о (1-р+pе")" O n(1 – p+ pe*) enpt
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