The average rate of job submissions in a busy computer center is 4 per minute. If it can be assumed that the number of submissions per minute interval is Poisson distributed, calculate the probability that: What is the probability that three jobs will arrive in one minute? What is the probability that three jobs will arrive in 30 seconds? At least 15 seconds will elapse between any two jobs. If no jobs have arrived in the last 30 seconds, what is the probability that a job will arrive in the next 15 seconds? What is the mean and variance of this distribution?