Suppose we choose a random point in the interval (-2, 1) and denote the distance to 0 by X. Prove that X is a continuous random variable.

2. Originally Posted by clockingly
Suppose we choose a random point in the interval (-2, 1) and denote the distance to 0 by X. Prove that X is a continuous random variable.
Define what you mean by a random point - no such thing without an
explict method for generating it.

Then define what you mean by a continuous random variable.

RonL

3. Originally Posted by clockingly
Suppose we choose a random point in the interval (-2, 1) and denote the distance to 0 by X. Prove that X is a continuous random variable.
If you begin with a random variable Y that is uniformly distributed on the interval (-2,1), then it is reasonable to think of Y as a randomly chosen point. Then by definition X=|Y|, Y’s distance from zero. Now one characterization of continuous random variable is: the range of the variable includes an interval of real numbers, bounded or unbounded. The range of X is [0,2).

4. Thanks, CaptainBlack and Plato for responding!

I was wondering - would I be correct by saying that the density of X is
1/(-2-1) = -1/3

and the mean of X is

(1+-2)/2 = 1/2

?

5. Originally Posted by clockingly
I was wondering - would I be correct by saying that the density of X is
Assuming that I am correct about Y being uniformly distributed on the interval (-2,1), and X=|Y| then the density function is a bit hard to see.
Consider this: $\displaystyle f(x) = \left\{ {\begin{array}{lc} {\frac{2}{3}} & {0 \le x \le 1} \\ {\frac{1}{3}} & {1 < x \le 2} \\ \end{array}} \right.$

You may want to check out the integral of f(x) over [0,2] to see how it all works.
In particular, you want use the integral of xf(x) to find the mean.