Question: Need detailed explanation !!! Consider the continuous random variable X with probability density function: f) = e-Xw) for x a 0, where k is a

Need detailed explanation !!!

Consider the continuous random variable X with probability density function: f\") = e-Xw) for x a 0, where k is a constant to be determined. (a) Let Y = |n(X). Find the range and probability density function of Y. (b) Using the result in (a), or otherwise, nd the value of k. (c) Find the 20th percentile of X. (d) Find the expected value and variance of X. Hint: you may nd this formula for completing the square useful when manipulating the integral: axz + bx + c = a ((x + 0.52m)2 + c/a 0.25b2/a2)

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