I need to compute 2 discrete distributions with equal mean and variance. One should be a distribution taking values x and y and the other one taking values z, 0, and y. The probabilities should take the following form:
- Distribution 1: takes values x and y. prob(x)=0.3; prob(y)=0.7
- Distribution 2: takes values y, z and v with Prob(y)=0.7; prob(v)=q; prob(z)=r. Y=6000; V=0.
The idea is to choose z and x so that both distributions have equal mean and variance.
I'm not an expert so I don't know if there are too many unknowns or if this is possible at all. What parameters could I change to make a solution possible? I would be very grateful for hints how to solve this.