Example 15C: The final mark (Y) for a particular statistics course comprises of a 30% weighting for the class record and a 70% weighting for the examination. A student believes that she is equally likely to obtain a mark anywhere between 45% and 65% for her examination (X). (a) Find the probability density function for her final mark (Y) if she has a class record of 50%. (b) Find the distribution function of her final mark. (c) Find the probability she gets a third-class pass (between 50% and 60%) as a final mark. (d) Find the probability that she gets a lower second (between 60% and 70%). (e) What is the probability that she fails (below 50%)?