A shop receives a shipment of 1000 cheaply made lamps. The probability that any individual lamp is defective is 0.001. Assume the defectiveness is independent for each lamp. Let X be the number of defective lamps in the batch of 1000. Calculate the expected value E(X) and variance Var(X). Enter your answer numerically and do not round. For example, if the number you got is 2/5, you should enter 0.4.
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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