If moment generating function of discrete random variable X is (q + pe^t)ⁿ, then E(X²) equal to

The correct answer is np(np + q).

Key Points

• A moment generating function is a mathematical tool that helps to calculate moments of a distribution (i.e. its mean, variance, etc.).
• In this case, the moment generating function of X is given by (q + pet)^n.
• To find the expected value of X^2, we can use the second derivative of the moment generating function and evaluate it at q = 0.

 Additional Information

• Moment generating functions are not always unique for a given distribution.
• The expected value of X^2 can also be found by directly calculating E(X^2) from the definition of expectation.

 Important Points

• Moment generating functions can be useful in cases where it is difficult to directly calculate moments of a distribution.
• The moment generating function can provide information about all the moments of a distribution.