Homework: Let \( Y_{1} \) and \( Y_{2} \) be two random variables with joint p.d.f: \[ f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{cc}1, & 0 \leq y_{1} \leq 2, \\ 0, & 0 \leq y_{2} \leq 1,\end{array} 2 y_{2} \leq y_{1},\right. \] Find: 1) \( P\left(Y_{1} \geq 0.5\right) \). 2) \( P\left(Y_{1} \geq 1.5 \mid Y_{2}=0.5\right) \).

The number of births in a hospital follows a Poisson distribution with an average number of 1 birth per hour. What is the standard deviation associated with the number of births within a whole day (i.e. over 24 hours)?

The number of births in a hospital follows a Poisson distribution with an average number of 1 birth per hour. What is the probability that there will be at least one birth within the next 2 hours? \( \frac{0.8647}{0.6321} \) 0.1353

In a town, the number of electric power failures occurs randomly with an average of one failure every 4 months. What is the variance associated with the number of failures over six consecutive months?

The number of births in a hospital follows a Poisson distribution with an average number of 1 birth per hour. What is the probability that there will be no birth within the next 2 hours? 0.250 0.135 0.368 1.00

A photographer was told that the average number of lion sightings on a 3-day safari is 1. What is the probability of not seeing any lion over the course of the 3-day safari? 0.368 0.000 0.500 0.333