1) Suppose the number of buses arriving at a stop follows a Poisson process with an average of 6 per hour. Let X be the time (in hours) you will have to wait for a bus once you arrive at the stop. What is P(X>0.25)?

2) Suppose a continuous random variable X has a cdf equal to k(x^3-x^2+4x-4) for x values between 1 and 2. For x1, the value of the cdf is 0. For x2, the value of the cdf is 1. What is k?

3) Let f(x)=3/(x^4) when x>1 and 0 otherwise. What is the variance of X?

4) Suppose the number of hours of sleep a person gets follows a Unif(7,9) distribution. What is the probability a randomly selected night of sleep lies within one standard deviation of the mean? Round to 2 decimal places.

5) Suppose Z has a standard normal distribution. According to the empirical rule, what is P(-2