Suppose that random observations are needed from the triangular distribution whose probability density function is f(x) 

(a) Derive an expression for each random observation as a function of the uniform random number r.

(b) Generate five random observations for this distribution by using the following uniform random numbers: 0.0956, 0.5629, 0.6695, 0.7634, 0.8426.

(c) The inverse transformation method was applied to generate the following three random observations from this distribution:
0.09, 0.64, 0.49. Identify the three uniform random numbers that were used.

(d) Write an equation that Excel can use to generate each random observation from this distribution.