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For a non-negative real number x, let [x] be the largest integer that is less equal to x. Let X be an exponential random variable

For a non-negative real number x, let [x] be the largest integer that is less equal to x. Let X be an exponential random variable with expectation 1.

(a) Find the density of X [X].

(b) Given that 0.4 X [X] 0.6, what is the conditional probability for [X] = 3?

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