Which of the following is not a valid probability distribution for a discrete random variable? Check all that apply.

A. 1/5,1/10 ,1/10 ,1/10 ,1/5 ,1/10 ,1/10 , 1/10

B. 1/3,1/4 ,1/5 ,1/6

C. 1/2,1/4 ,1/8 ,1/16 ,1/32 ,1/64 ,1/128 ,1/128

D. -1/2, -1/3, -1/4, -1/5, 137/60

E. 1/6, 1/6, 1/6, 1/6, 1/6, 1/6

Question

Which of the following is not a valid probability distribution for a discrete random variable? Check all that apply.

A.	1/5,1/10 ,1/10 ,1/10 ,1/5 ,1/10 ,1/10 , 1/10

B.	1/3,1/4 ,1/5 ,1/6

 C.	1/2,1/4 ,1/8 ,1/16 ,1/32 ,1/64 ,1/128 ,1/128 

D.	-1/2, -1/3, -1/4, -1/5, 137/60

E.	1/6, 1/6, 1/6, 1/6, 1/6, 1/6

tkhunny · Answer

Discard D. immediately.  Negative numbers are not allowed.

What other criterion is definitive?

anonymous · Answer

well anything that you could count because we are looking for measurements

tkhunny · Answer

??  I don't know what that means.

The must add to unity.

E. 1/6 six times is 1.  Perfect.

Try the others.

anonymous · Answer

well A. is 7/10ths and I'm not to sure about C.

tkhunny · Answer

A. is not 7/10.  The are 6 at 1/10 and 2 at 1/5 = 2/10.  That one looks good.

tkhunny · Answer

C. Is fun.  Think backwards on it.  We have to get to 1

Start with 1 and subtract things off.

1 - 1/2 = 1/2
1/2 - 1/4 = 1/4
1/4 - 1/8 = 1/8
etc...

anonymous · Answer

so 1/2, 1/4, 1/8, 1/16, 1/32, 1/64?

tkhunny · Answer

1/8 - 1/16 = 1/16 <== That's how much there is left.
1/16 - 1/32 = 1/32  <== Now, there is just this much left.
1/32 - 1/64 = 1/64
1/64 - 1/128 = 1/128
1/128 - 1/128 = 0 and we are done.

That one summed to unity.

anonymous · Answer

I think I'm starting to get it now

anonymous · Answer

How about B. ?

tkhunny · Answer

You really just have to find a way to add them up.  I used decimals.

1/3,1/4 ,1/5 ,1/6

Using hundreths
1/3 is 33ish
1/4 is 25, giving now 58ish
1/5 is 20, giving now 78ish
Well, we have 22 hundreths to go.  Will 1/6 cover it?

anonymous · Answer

no it only gives 16 right?

tkhunny · Answer

Yup.  that one is a little short.

We used a different method to add each of them.  Stay flexible!!

anonymous · Answer

so what method did you use?

tkhunny · Answer

All available.  Whatever seemed most appropriate for the given set of data.

anonymous · Answer

alright so A, C, and E are not a valid probability distribution for a discrete random variable?

anonymous · Answer

Right?

tkhunny · Answer

Backwards.  We disqualified B. and D.

anonymous · Answer

yes that's right

anonymous · Answer

oh I get it

tkhunny · Answer

Are they all positive?
Do they sum to unity (1)?

Done.