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For any discrete random variable X, with probability mass function
 define the polynomial function 
For a certain discrete random variable Y, there exists a scalar β ∈ [0,1] such that gY (z)= (1 - β + βz)
N
The expectation of Y is
  • a)
    Nβ(1 - β)
  • b)
  • c)
    N(1 - β)
  • d)
    Not expressible in terms of N and β alone
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
For any discrete random variable X, with probability mass functiondefi...
Derivative of gx(z) evaluated at z=1 gives expectation E(X) of X.
Therefore, take derivative of gY(z) with respect to z, and plug in z=1
Derivative is N.β.(1 - β + βz)(N-1), plug in z = 1, gives Nβ.
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For any discrete random variable X, with probability mass functiondefine the polynomial functionFor a certain discrete random variable Y, there exists a scalar β ∈ [0,1] such that gY(z)= (1 - β +βz)N.The expectation of Y isa)Nβ(1 - β)b)Nβc)N(1 - β)d)Not expressible in terms of N and β aloneCorrect answer is option 'B'. Can you explain this answer?
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For any discrete random variable X, with probability mass functiondefine the polynomial functionFor a certain discrete random variable Y, there exists a scalar β ∈ [0,1] such that gY(z)= (1 - β +βz)N.The expectation of Y isa)Nβ(1 - β)b)Nβc)N(1 - β)d)Not expressible in terms of N and β aloneCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about For any discrete random variable X, with probability mass functiondefine the polynomial functionFor a certain discrete random variable Y, there exists a scalar β ∈ [0,1] such that gY(z)= (1 - β +βz)N.The expectation of Y isa)Nβ(1 - β)b)Nβc)N(1 - β)d)Not expressible in terms of N and β aloneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any discrete random variable X, with probability mass functiondefine the polynomial functionFor a certain discrete random variable Y, there exists a scalar β ∈ [0,1] such that gY(z)= (1 - β +βz)N.The expectation of Y isa)Nβ(1 - β)b)Nβc)N(1 - β)d)Not expressible in terms of N and β aloneCorrect answer is option 'B'. Can you explain this answer?.
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