which one of the following probability mass function can define a probability distribution?

Question

a) $f(x)=(5-x^2)/6$ for $x=0,1,2,3$
b) $f(x)=x/15$ for $x=1,2,3,4,5$
c) $f(x)=1/2^x$ for $x=0,1,2,3,4$
d) $f(x)=1/4$ for $x=2,3,4,5,6$

Can you please suggest me how to solve these questions ?

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score 2 · Answer 1 · answered Oct 30 '13 at 15:41

2

For a function $f:\mathbb{R}\to\mathbb{R}$ to be a valid probability mass function it must satisfy $f(x)\geq 0$ for all $x$ and $$\sum_{x\in\, \mathrm{supp}_f} f(x)=1,$$where $\mathrm{supp}_f=\{x\in\mathbb{R}\mid f(x)>0\}$.

answered Oct 30 '13 at 15:41

Stefan Hansen

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score 0 · Accepted Answer · answered Oct 30 '13 at 15:43

0

Hint: The probabilities should sum to 1 and all be non-negative. Which of your alternatives satisfy these two conditions?

answered Oct 30 '13 at 15:43

hejseb

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Thanks for the help. I found my answer. – PallaviBatra Oct 30 '13 at 16:03

which one of the following probability mass function can define a probability distribution?

2 Answers2