Question 3. (6 marks). Consider the following function: 121-63: if 2 g a: g 4, at) 2 5335 if 5 S a: g 6, 0 otherwise. (a) Sketch the graph of at) on a suitable range of a: values. (b) Explain why f is a valid probability density function. Now assume that Z is a random variable whose probability density function is f. (c) Use your graph and properties of probability to determine each of the following: (i) P(Z 2 4) (d) You are given the following: if 2 S a: g 4, then P(Z g .r) = W. Determine similar formulas for P(Z g :6) when 4