A traffic light at a certain intersection is green 60% of the time, yellow 10% of the time, and red 30% of the time. A car approaches this intersection once each day. Assume that each day represents an independent trial. Answer the questions below: (a) Let Y denote the number of days up to and including the third day on which a red light is encountered. Find P(Y = 7). (b) What is the probability that in a sequence of 10 days, four green lights, one yellow light, and five red lights are encountered?
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!
A traffic light at a certain intersection is green 60% of the time, yellow 10% of the time, and red 30% of the time. A car approaches this intersection once each day. Assume that each day represents an independent trial. Answer the questions below: (a) Let Y denote the number of days up to and including the third day on which a red light is encountered. Find P(Y = 7). (b) What is the
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