Problem 1. Consider the experiment of tossing a biased coin 5 times. Let the probability of heads be 0.4. Let the random variable X denote the number of heads.
What is the probability of the coin turning up tails?
What are the values this random variable can take?
Is it a discrete or a continuous random variable?
What is its probability distribution function? Is it uniform? If not, what is it?
What is the expected value?
Consider instead that the coin was tossed 1000 times, what would be the expected value of the number of heads?
Problem 2. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
Compute the probability of receiving three calls in a 5-minute interval of time.
Compute the probability of receiving exactly 10 calls in 15 minutes.
Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time? What is the probability that none will be waiting?
If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?