A system component has malfunctioned, and the delivery time, Y, of a new part is uniformly distributed on the interval of 0 to 3 days; i.e. it can arrive at anytime over the ext three days. The system must be shut down until the new part arrives. The cost incurred (in thousands of dollars) due to this interruption is C = 5+ 2Y². a. Find the probability that the cost incurred due to the interruption is less than $13,000. (Hint: Think in terms of days or use P(g(Y) < c) = P(Y < g¬'(c)).) b. Find the expected value of C. c. Find the standard deviation of C.
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!
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