Discrete Random Variable Whose Set of Values Is Finite or Countable

Running Head: DISCRETE RANDOM VARIABLES 1

DISCRETE RANDOM VARIABLES 2

Discrete Random Variables
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DiscreteRandom Variables
Introduction
The discrete random variable refers to a variable that can only account for only countable values. For instance, we can flip a coin as many times as we can and be eligible enough to count both the number of heads and tails easily without difficulty. Therefore, the number or heads will be either 0, 1, 2, 3, 4,,, and plus infinity. Therefore, this numbers will not be in a fraction form but as a whole number. Therefore, the number of counts of the heads is a discrete random variable because it is as a result of a random process of flipping the coin.
Article one
According to this article, the probability histogram distribution tables play a key role in statistics and probability. These types of tables allow an individual to tally all types of numbers and information that fall into numerous ranges. This type of information will be extremely beneficial to the fiscal analysis of the number of times the coin was flipped to make sound and fiscal decisions when drawing the Xavier and Yves histogram at the end of the probability taking over the attached charts and tables(Bolt.mph.ufl.edu, 2016).
From this article, it is easy to notice that, as the number of times the coin is being flipped, the rate of probability increase with an increase in flipping according to the probability histogram drawn in this website. Therefore, from this probability histogram, it is noticed that the sum of all the probabilities is equal to the area of the histogram drawn and therefore, it can be denoted that the total of all odds must be equal to one(Bolt.mph.ufl.edu, 2016).
From the example of changing majors in this article, asking about the probability of a randomly selected senior, whereby the selected senior has changed the seniors more than once, the sum of the changing seniors is equal to the selected majors (X=x) and therefore, the probability is to be denoted as (p(X=x)). However, when calculating the probability more than once, it is denoted as (p(X>1))(Bolt.mph.ufl.edu, 2016).
With regard to the statistical principal from this article, in exploratory data analysis, various data collection principals have been used such as mean, variance and standard deviation methods in calculating the discrete random variables. Moreover, in this article, Xavier production lines are used to interpret the likes of standard deviation and therefore, this lines can be of help when developing a conclusion pertaining a given discrete random variable. Also, from this article it is clear that, distribution histograms can easily be drawn only after the Xavier production lines have been formulated and drawn for emphasis. Finally, this article formulates a very significant statistical principal which states that means and standard deviations are some of the approaches used to assess which discrete random variable values are unusual. Example, if the interval values are -0.33 and 4.58, the negative value is assumed since there is no defective parts in discrete random variables and therefore, if our designated value is 4, therefore 4 is not an unusual number and 5 is an unusual number(Bolt.mph.ufl.edu, 2016).
Article 2
You can actually approach discrete random variables as if they were continuous that is, (define density for discrete variables) with the little help of delta function. As emphasized from this article, for rigorous treatment you’ll need a lot of technical details (theory of generalized functions), though you don’t need it in practice. However it is significantly important to note that marginalization is effectively taking an expectation of conditional density (or probability): p(x) = int p(x, y) dy = int p (x|y) p(y) dy = E_y p (x|y) Here we don’t use any assumptions about p (x|y), it can be discrete or continuous doesn’t matter. I do assume that y is continuous, but the same result holds for discrete version, so If y was discrete, you’d just use sum instead of an integral when taking expectation. So, the rule is simple: whenever you marginalize, use summation operator that corresponds to the type of a variable you marginalize over (sum for discrete, integral for continuous). Therefore, from this article it is clear that, In order to compute joint distribution you just use chain rule (the one from probability, don’t confuse it with the one from calculus) backward(Gaussian, 2012).
From this article, the example of plotting the CDF and the PDF is a simplified for of discrete uniform random variable whereby the intercepting points amidst the X and Y axis are the only regions that offers the required variables. Moreover, with reference to the distribution histograms in this article, they are generated with almost equal probability just as the histogram distribution table from the other article(Gaussian, 2012).
Finally, the above two articles are completely the same except that each one of the employs a different approach of determining the discrete random variable. For instance, the first article employs the use of the Xavier and Yves production lines, variance and standard deviation while the second article employs the use of the probability mass function and the probability density function.

Reference
Bolt.mph.ufl.edu,. (2016). Discrete Random Variables » Biostatistics » College of Public Health and Health Professions » University of Florida. Retrieved 4 February 2016, from http://bolt.mph.ufl.edu/6050-6052/unit-3b/discrete-random-variables/
GaussianWaves,. (2012). Uniform Random Variables and Uniform Distribution. Retrieved 4 February 2016, from http://www.gaussianwaves.com/2012/09/uniform-random-variables-and-uniform-distribution/