Discrete Random Variables - pmf

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!!

Re: Discrete Random Variables - pmf

Quote:

Originally Posted by

**Matt1993** 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!!

Hi Matt1993! :)

What is the reason you think that -1/3 =< theta =< 1/3?

That is likely the key to the proof...

Re: Discrete Random Variables - pmf

See all I did was let the pmfs equal zero and then I just tried values until I came up with that answer. That's the problem

Re: Discrete Random Variables - pmf