Question

The distance X between trees in a given forest has a probability density function given f (x) cex/10, x >0, and zero otherwise with measurement in feet i) Find the value of c that makes this function a valid probability density function. [4 marks] ii) Find the cumulative distribution function (CDF) of X. 5 marks What is the probability that the distance from a randomly selected tree to its nearest neighbour is at least 15 feet. iii) 4 marks) iv) Find the mean and variance of X. (7 marks
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-メ! (x) =ce (Li) 、Tw (d f of (x) (XEX) = 反(X) =11-e Lit) 1.5 (iv) 1 0 lo

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