Question
Let S={s1,s2,s3,s4}
be a sample space with probability distribution P,
given by
P(s1)= 0.5, P(s2)= 0.25, P(s3)= 0.125, P(s4)= 0.125.
There are sixteen possible events that can be formed from the elements of 'S'.
Compute the probability and surprise of these events.
be a sample space with probability distribution P,
given by
P(s1)= 0.5, P(s2)= 0.25, P(s3)= 0.125, P(s4)= 0.125.
There are sixteen possible events that can be formed from the elements of 'S'.
Compute the probability and surprise of these events.
Answers
I assume that each of the sixteen events has two outcomes of S, namely
P(s1,s1), P(s1,s2).....P(s4,s4).
By the multiplication rule, and assuming that the two outcomes are independent, we have
P(s1,s1)=P(s1)P(s1)=0.5*0.5;=0.25
....
P(s4,s4)=P(s4)P(s4)=0.125*0.125=0.015625
Note: The sum of probabilities of the 16 events should add up to 1.
Not sure about the surprise part.
P(s1,s1), P(s1,s2).....P(s4,s4).
By the multiplication rule, and assuming that the two outcomes are independent, we have
P(s1,s1)=P(s1)P(s1)=0.5*0.5;=0.25
....
P(s4,s4)=P(s4)P(s4)=0.125*0.125=0.015625
Note: The sum of probabilities of the 16 events should add up to 1.
Not sure about the surprise part.