(Solved): Let \( x \) be a Poisson random variable with mean \( \mu=2 \). Calculate \( P(x=1) \) (Very impor ...

Let \( x \) be a Poisson random variable with mean \( \mu=2 \). Calculate \( P(x=1) \) (Very important: please roundup to 3 decimals). Let \( x \) be a Poisson random variable with mean \( \mu=5 \). Calculate \( P(x>1) \) (Very important: please roundup to 3 decimals). Let \( x \) be a binomial random variable with mean \( n=20 \) and \( p=0.1 \). Use the Poisson approximation to calculate \( \mathrm{P}(\mathrm{x} \leq 2) \) (Very important: please roundup to 3 decimals).