1. In probability theory, a normal (or Gaussian or Gauss or LaplaceGauss) distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is 1 1(x-u)2 9? T F(x) = a 211' Estimate the probability distribution given the empirical equation for Normal Distribution below from X1 = -2 up to X2 = 1.6 using Multiple application Trapezoidal Rule for the following segments n = 4, 8, 12, and 16. Show the step- bystep solution and tabulate the results. P(x) = [big202 dx x1 V21: 7. Estimate the derivative of the function in problem (1) at the x = 0.75 using the following step sizes h = 0.125, h = 0.0625 and h = 0.03125 for the following techniques forward finite, backward finite and centered finite divided difference. Use both the truncated and more accurate derivative estimate formulas. Improve the truncated derivative estimates using Richardson's extrapolation in each of the approximate derivative techniques. Show the step- by-step solution and tabulate the results