Question

Determine the required value of the missing probability to make the distribution a discrete probability distribution.

x	p(x)
3	0.32
4	?
5	0.29
6	0.12

Answer 1

We know that for a discrete probability distribution, the total probability is always equal to 1, i.e.,

where P(x) = P(X=x), where x is the mass point of the discrete probability distribution.

Now, let P(4) = P(X=4) = c. So we must have

P(3) + P(4) + P(5) + P(6) = 1

or, 0.32 + c + 0.29 + 0.12 = 1

or, c + 0.73 = 1

or, c = 1 - 0.73

or c = 0.27

P(4) = P(X=4) = 0.27 , which is the required answer.

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