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# Cumulative Distribution and Probability Density Function and Expected Value

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1. Let X be a continuous random variable, with
P(X>x) = (1-x)^2 0&#8804;x&#8804;1
(i) Find the cumulative distribution function of X.
(ii) Find the probability density function of X.
(iii) Find the expected value of X.

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#### Solution Preview

(i) since the cumulative distribution function (cdf) is the probability that the variable takes a value less than or equal to x. That is ...

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Cumulative Distribution and Probability Density Functions and Expected Values are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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