(\Triangular" distributions.) Let X be a continuous random variable with prob- ability density function f(x). Suppose that all we know about f is that a </= X </= b, f(a) = f(b) = 0, and that there exists a value c between a and b where f is at a maxi- mum. A natural density function to consider in this case is a piece-wise linear function, corresponding to lines connecting (a; 0) with (c; f(c)), and (c; f(c)) with (b; 0). a) What is the value of f(c)? b) Sketch a graph of f(x). c) Compute the expected value E(X) and the variance Var(X). I have not been given any numbers and am very confused as to how there could be a numerical answer to this question. I know the probability density function looks like a triangle, with f(a) and f(b) on the x-axis, but am not sure where to go with this. Anyone have a suggestion?