The discrete random variable R takes the values in S = { -3, -1, 1, 3 } with probabilities respectively,
( 1 - theta )/4, ( 1 - 3theta) /4, ( 1 + 3theta)/4, (1+ theta)/4,
where theta is a real constant. Find the range of values for which this is a valid probability mass function.
i think the answer is -1/3 =< theta =< 1/3
BUT HOW DO PROVE IT!!!!!!!
help!!
That's close.
The axioms of probability (see wiki) require in particular 2 things from the probabilities:
- Each probability is at least 0: .
.- The sum of all probabilities is 1: .
In your case that means: