(11) Use the commonly stated form of Chebyshev's inequality to find an upper bound to P(X > 300) when X ~ Poisson(10). (a) Note that P(X > 300) = P(X > 300) + P(X < -300), since P(X < -280) = 0. so, we have Std(X) VIO = 0.010540925. P(X > 300) = P(|X| > 300) < 300 300 (b) Note that P(X > 300) = P(X > 300) + P(X < -300), since P(X < -280) = 0. So, we have Var(X) 3002 10 = 0.00011111. 3002 P(X > 300) = P(|X| > 300) < (c) Cannot be done, since Chebyshev's inequality can only be applied when two sided tail probabilities are sought. (d) Note that P(|X – 10| > 290) = P(X > 300) + P(X < -280), since P(X < –280) = 0. So, we have P(X > 300) = P(|X – 10| > 290) < Var(X) 10 = 0.000118906. - 2902 2902 (e) None of the above. The correct proof is (a) (b) (c) (d) (e) N/A (Select One)
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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