what is the random variable of this

[calcnoob]

I have to calculate the random variable X if P(X=0.1)=0.4 and P(X=1.2)=0.1

so it's a step function and I've calculated the expected value and variance but I don't know how to come with the actual random variable itself. I think it's a step function and I use the inverse transform method but I only know how to use it for curves on the distribution function and it the P(X=is a constant) because the random variable will always be the constant but what about in this situation?

 

[HallsofIvy]

First, what do you mean by "calculate the random variable X"? X is, as you say, a variable and does not have a specific value unless you are given other information. Also, you must have other information about P(X). What you give makes it seem like X takes on only the two values, 0.1 and 1.2, but that is clearly not true because the probabilities given do not add to 1.