Suppose your waiting time for a bus in the morning is uniformly distributed on [0, 10], whereas waiting time in the evening is uniformly distributed on [0, 12] independent of morning waiting time. (a)If you take the bus each morning and evening for a week, what is your total expected waiting time? (Assume a week includes only Monday through Friday.) [Hint: Define rv's X1,... , X10 and use a rule of expected value.] Total Time= min (b) What is the variance of your total waiting time? (Round your answer to two decimal places.) Variance of Wait Time= min2 (c) What are the expected value and variance of the difference between morning and evening waiting times on a given day? (Use morning time − evening time. Round the variance to two decimal places.) expected value = min variance= min2 (d) What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for a particular week? (Use morning time − evening time. Assume a week includes only Monday through Friday.) expected value = min variance= min2

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!