Question 4. (5 marks). For this question, we will say that a continuous random variable X follows a mystery distribution with parameters a and b (with a, b > 0) if the probability density function for X is given by fx (z) = I (2) 46. ((2 ) 4 + 1 ) - 6 - 1 if x > 0 otherwise. In that case, we write X ~ Mystery(a, b). (a) Write an R function dmystery with three arguments x, a and b, which computes this probability density function. Ensure your function is vectorised for the remaining parts of this question; you may use Vectorize as in the lab classes. Use correct syntax to define a function, i.e., dmystery 2.604) (iii) P(1.906