Question

Q91

What is the probability that a continuous random variable will take on any specific value? Explain your answer. [1 Mark]

VERY IMPORTANT:

USE WORD FORMAT - NO HANDWRITTEN ANSWER WILL BE ACCEPTED.  

NO PLAGIARISM - QUESTION WILL BE SEND BACK FOR REFUND WITH POOR RATING.

Answer 1

The probability is zero.

Explanation:

If a random variable(say X) is continuous , it is has a corresponding probability density function f(x) that is defined as:

                                   

                                 P (X≤a)= _{-∞afxdx      ……….i}

^{where -∞<a<∞.}

According to the standard Kolmogorov axioms of probability,

                  ^{-∞∞fxdx=1}_{…………………..ii}

This is because the probability of the sample space is always unity.

Moreover, f(x)≥0.

The possibility that X takes on a specific value a is given by:

P(X=a)= Number of favorable outcomes

                Number of possible outcomes

             =aafxdx /   -∞∞fxdx = 0/1=0     (from equations i and ii)

The area under the graph of the probability density function is 0 if the interval shrinks to a single point.