For this assignment, you are free to use the software of your choice: Excel, Mat

Question

For this assignment, you are free to use the software of your choice: Excel, Matlab, Minitab, C++… or any other option that you find suitable. You must explain which software you use, what is the code that you input, and what is the result (numerical value).

In the file data1, there are two tabs

this is the link of file data1 https://www.mediafire.com/?0u97nzga2hc6lmm

Single discrete random variables [17 pts]

In the first tab (single discrete variables) you will find the values taken by two independent variables, X and Y over 200 experiments.

Compute first the values taken by the random variables S, L and P where S=X+Y, L=X+2*Y and P=X.Y. [3pts]
For each variable X, Y, S, L and P:

Compute the average value [5pts]
Compute the variance [5pts]
Compute the standard deviation [2.5pts]

What do you observe? [1.5pts]

Joint probability function [18 pts]

In the second tab, you find the values of a joint probability mass function over X and Y. The first row indicates the values taken by X (from -10 to 10) and the first column the values taken by Y (from 0 to 30). The inner values represent fXY(x,y).

Verify that this is indeed a joint probability mass function. [1 pt]
Give the marginal probability mass function fX and fY. [3 pts]
Compute the mean, variance and standard deviation of these marginal distributions. [5 pts]
Give the conditional probability distribution fX|10 and fY|2. [4 pts]
Compute the covariance and correlation between X and Y. [3 pts]
Are X and Y independent? [2 pts]

Explanation / Answer

For this assignment i am using R programming language.

The average value:

For variable X : 17.44

For variable Y : 17.17406

For variable S : 34.61406

For variable L : 51.78811

For variable P : 299.2621

The variance :

For variable X : 17.33307

For variable Y : 11.8629

For variable S : 28.68649

For variable L : 63.76572

For variable P :   8990.38

the standard deviation:

For variable X : 4.1633

For variable Y : 3.444256

For variable S : 5.355977

For variable L : 7.985344

For variable P : 94.81761

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