1) Suppose that Y has a Poisson distribution with mean=0. Compute Pr(Y>=1)
2)Consider the random variable Y=1/X where X is uniform into (0,1).What is the median of Y?
2) The cdf of Y is $\displaystyle F(y) = \Pr\left( Y < y\right) = \Pr\left( \frac{1}{X} < y\right) = \Pr\left(X > \frac{1}{y}\right) = \int_{1/y}^1 dx = 1 - \frac{1}{y}$.
If $\displaystyle m$ is the median of Y then $\displaystyle F(m) = \frac{1}{2} \Rightarrow 1 - \frac{1}{m} = \frac{1}{2} \, ....$