3 suppose s is a countably infinite sample space ie si s2 s

3. suppose s is a countably infinite sample space, i.e., { si, s2, s3 ). Is it possible to define a equiprobable probability measure on S? Justify your answer carefully. (Hint: think about the axioms, and consider two cases: (j) P(s1) = 0 and (ii) P(s1) > 0.)

Solution

When the S is a infinite sample space, to construct a probability measure for the experiment of choosing a point at random from S. We take a universal set U to be in S, and under the equiprobable probability measure we now define the probability of an event A as P(A)=|A|/|S| whenever A is an interval. The probability measure is said to be uniform.We may extend this concept to any number of dimensions.