Is this rectangular ?

[vinayan]

Consider the following rectangular distribution

f(x) = 2 , 0 < x < 1/2
= 0 , elsewhere.

Please suggest whether this is a geuine distribution or whether this violate the condition that probability should be always in between 0 and 1.

[jerryb]

this is a valid distribution.

recall that the sum of probabilities of all outcomes equals 1. if you intergrate the area under the curve you will find a total area of 1, further since there is an infinite number of outcome between zero and 1/2 (its a continuous random variable) the probability of any particular outcome is zero, therefore all individual outcomes have a probability of zero which is less than or equal to 1.

just as a technicality, the probability of any out come must be greater than or equal to zero and less than or equal to 1.

cheers
jerry

[vinayan]

Thank you very much!!!