PLEASE ANSWER NO. 3

1. In probability theory, a normal (or Gaussian or Gauss or Laplace-Gauss) distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is 1 F(x) e3(4)? 2 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- by-step solution and tabulate the results. X2 1 P(x) = x 211 X 1 - Le Le 2(x) dx = 3. Estimate the probability distribution on problem (1) using Multiple application Simpson's 3/8 rule for the following segments n = 6, 9, 12 and 15 segments. Show the step-by-step solution and tabulate the results