Question

How to show a random variable is not an uniform variable? In particular, please show that:...

How to show a random variable is not an uniform variable?

In particular, please show that:

X1 is uniform in [0, 1], X2 is uniform in [1, 2], but X1+ X2 is not uniform variable.

Math   Statistics-And-Probability   
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Answer #1

If a random variable has an equal probability for taking any value of its sample space then such a random variable is called uniform random variable

To show that a random variable is not a uniform random variable just show that all the elements in its sample don't occur with equal probability

let

Given

Y can take values between 1 and 3

For Y to take value 1, there is only one possibility when

Similarly for Y to take value 3, there is only one possibility when

But for the rest of the values there are more than one possibilities

We can observe that all values of Y are not equally likely to occur

Therefore we can conclude that does not follow a uniform distribution

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