Statistics and probability - the basics

Question

With $x$ assuming random values if $1$, $2$, or $4$ and if you know the expected value of $x$ is equal to $2.7$. If you are only given one other piece of information $P(X=1) = 0.3$ then how can you find $p(x=2)$ and $p(x=4)$? I tried working backwards knowing the $e(x)$ but don’t think I have enough information. Thanks!

Answer 1

HINT: You have a system of three equations with three unknowns: $$\mathbb E[X]=P(X=1)+2P(X=2)+4P(X=4)=2.7$$ $$P(X=1)=0.3$$ $$P(X=1)+P(X=2)+P(X=4)=1$$ The third equation is probably the only one that you were missing.