Probability (Expectation)

Question

Suppose that the expectation of a random variable X is 5. Which of the following statements is true?

(A) - There is a sample point at which the X has the value 5.

(B) - There is a sample point at which the X has the value greater than 5.

(C) - There is a sample point at which the X has the value greater than or equal to 5.

(D) - None.

Explain.

Answer 1

Lets consider each option:

option A) This neednt be because there can be a point at which the value of random variable can be greater than 5 but probablity is less than 1.

 

option B) This neednt be as there can be a signle point whose value is 5 with probablity 1.

 

option C) If all points have value less than 5, how can the expectation be equal to be ? So, this must be true.

 

So, answer is option (C).

Comments

Perfect