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Continuous random variable

(e) A continuous random variable X has the probability density function given by: f(x) = ( 2x/√ k for 0 ≤ x ≤ 2 0 otherwise. 

i. Show that the constant k equals 16. 

ii. Find the expected value of X. iii. Find the variance of X. 

iv. Derive the cumulative distribution function, F(x). 

v. Calculate P(X < 1 | X < 1.5)

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