Q1. Use N(0, 1), N(1, 4), N(5, 9) and N(-5, 16) to generate Chi-square distribution (degree of freedom: 4). Following is an example of Chi-square pdf with the sigma has different value of 2 and the mean values vary from 0 to 4.
Q2. A stock broker makes a deal with a client that the client will pay the broker a 20% "reward" of any profit the broker makes for him, and will pay the broker nothing if the broker loses money for the client. The stock portfolio profit is a normal distribution with a mean of zero and a standard deviation of $2. Use the resulting histogram to calculate the expected value of the reward. (Note that has a Gaussian distribution with mean and standard deviation can be generated using the "randn" function in MATLAB as following: NOTE 2.A random variable x= randn*σ + μ)
Q3. The range, r, of a cannon projectile under the influence of gravity, g=9.81 m/s2, and fired with muzzle velocity v0 = 10 m/s is determined by the angle its barrel makes with the ground, 0. From your Physics classes you will recall that the range is calculated as: r(v)= 2(v0)2/gsin v cos(v). If a wind of velocity 2 m/s2/ blows against the project, what will be the r(v)? Assuming that v is a random variable uniformly distributed between 0 and π/2, generate the probability density of the range f(r), through stochastic modeling. Use the resulting histogram to calculate the mean range of the projectile.
In report, you have to submit your code and the results (graphics).