The lifetime of a machine part has a continuous distribution: Osxs 40 fx(x) = { (10 + x)² else a. Calculate the probability that the lifetime of the machine part is more than 4. b. Calculate the expectation of life of this machine c. Calculate the variance d. Calculate the probability that the lifetime of the machine part is more than 4 given that lasts for less than 12

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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!