A random variable X that is gamma distributed with shape k and scale is denoted by x-1(k,6). The probability density function of the random variable that is gamma distributed is given by f(x;k,0)= Or(k) x>0 and k 0 > 0 where I'(k)=(k-1)! is the gamma function evaluated at k. a) b) By using probability density function calculate fourteen equally spaced points in the intervals x [1,10] for k=9 and 0 =0.5. Find the Newton interpolation polynomial that curve fits the data for each interval. Output the coefficients of the polynomial. Illustrate the individual points and Newton polynomial function in a) and b), respectively on a single plot. Fit the data obtained in b) by using quadratic spline for the intervals x [1,10] for k=9 and 0 =0.5. d) Illustrate the individual points and quadratic spline function in a) and d), respectively on a single plot f) Justify your result