If a random variable $X$ has an exponential distribution determined by parameter $\lambda = 1$, provide a function $t$ such that $t(X)$ has the distribution of the outcome of flipping a fair, six-sided cube.
I don't know how to approach this question. The first thing that jumps out at me is that we are attempting to transform a continuous random variable to a discrete one on the interval $[1, 6]$. Any suggestions/derivations would be incredibly helpful.
Here's a similar situation. The median of $X$ is $\log2$, i.e., $P(X<\log2)=P(X\ge\log2)=.5$. So the function $x\mapsto t'(x)$ that takes the value $0$ when $x<\log2$ and $1$ when $x>\log2$ is like a fair coin flip.