Moment Generating Function MCQ Quiz - Objective Question with Answer for Moment Generating Function - Download Free PDF

Last updated on Apr 9, 2025

Latest Moment Generating Function MCQ Objective Questions

Moment Generating Function Question 1:

A random variable X has the probability density function given by f(x)=14, -2 < x < 2. The moment generating function of X is given by

  1. e2t+e2t4t
  2. e2te2t4t
  3. e2t+e2tt
  4. e2te2tt

Answer (Detailed Solution Below)

Option 2 : e2te2t4t

Moment Generating Function Question 1 Detailed Solution

Concept:

The moment generating function of X is given as:

MX(t)=x1x2etxf(x) dx

Calculation:

MX(t)=22etx14 dx

MX(t)=14[etxt]22

=e2te2t4t

Top Moment Generating Function MCQ Objective Questions

A random variable X has the probability density function given by f(x)=14, -2 < x < 2. The moment generating function of X is given by

  1. e2t+e2t4t
  2. e2te2t4t
  3. e2t+e2tt
  4. e2te2tt

Answer (Detailed Solution Below)

Option 2 : e2te2t4t

Moment Generating Function Question 2 Detailed Solution

Download Solution PDF

Concept:

The moment generating function of X is given as:

MX(t)=x1x2etxf(x) dx

Calculation:

MX(t)=22etx14 dx

MX(t)=14[etxt]22

=e2te2t4t

Moment Generating Function Question 3:

A random variable X has the probability density function given by f(x)=14, -2 < x < 2. The moment generating function of X is given by

  1. e2t+e2t4t
  2. e2te2t4t
  3. e2t+e2tt
  4. e2te2tt

Answer (Detailed Solution Below)

Option 2 : e2te2t4t

Moment Generating Function Question 3 Detailed Solution

Concept:

The moment generating function of X is given as:

MX(t)=x1x2etxf(x) dx

Calculation:

MX(t)=22etx14 dx

MX(t)=14[etxt]22

=e2te2t4t

Moment Generating Function Question 4:

Consider the ordinary generating function of a sequence {an}n=0 be 1+z(1z)3. What is the value of a+ a+ a+ a3 + a4?

Answer (Detailed Solution Below) 55

Moment Generating Function Question 4 Detailed Solution

Formula:

(1x)n=1+n1!x+n(n+1)x22!+n(n+1)(n+2)x33!+

Calculation:

1+z(1z)3=(1+z)(1z)3

=(1+z)[1+3z1!+12z22!+60z33!+]

=(1+z)[1+3z+6z2+10z3+]

=1+3z+6z2+10z3+..+z+3z2+6z3+

=1+4z+9z2+16z3+25z3

Here an is the coefficient of zn

a= 1, a1 = 4, a2 = 9, a3 = 16, a4 = 25

so, 1 + 4 + 9 + 16 + 25 = 55

The value of a+ a+ a+ a3 + ais 55.

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