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INTRODUCTION:
As per the random variable definition, these are mathematical quantities or variables whose future result depends on any random event or experiment, whereas the result is unpredictable. Overall, the random variables are a representation of a probability or an outcome of chance. Random variables are represented with letters for a better understanding. The random variable is a clear representation of probability. Based on this it is categorised into two types, discrete random variable, and continuous random variable. Random variables play a vital role in the financial market as the probability is the foundation of rising and falling in the security pricing and the risks factor in an investment.
RANDOM VARIABLE DEFINITION?
The random variable is a mathematical expression of a value whose result or outcome depends upon various unpredictable and random events. The random variable is expressed by alphabetic letters for better understanding.
TYPES OF RANDOM VARIABLES:
On the basis of probability, the random variables are categorised into two groups,
- Discrete random variable: Discrete random variables are those variables that have a finite number of values, i.e., they could be counted and limited. For example, tossing of a coin discussed is a discrete random variable because the number of the outcome of getting ahead or tail is limited to the number of times the coin is tossed, i.e., if it is tossed three times, the variable can be limited between 0, 1, 2, and 3.
- Continuous random variable: Continuous random variables are the outcome of various random events or experiments which give a value that is not limited or certain. One of the basic examples of a continuous random variable is the stock market. In the stock market, the outcome is unpredictable, and the value is infinite.
RANDOM VARIABLES EXAMPLES:
There are several random variable examples in our everyday life. When it comes to probability and random variables, tossing a coin is one of the most general examples. Considering a fair coin-flip, what could be the probability of getting a head or a tail. On a flip, the probability of getting a head is 1 or 0. So considering X as the random variable:
X(a)=1, if a= heads :: 0, if a= tails.
Therefore, the probability mass function fy will be expressed as:
fy(a)={1/2, if a=1 :: 1/2, if a=0.}
Similarly, rolling dice is an example of random variables. A dice has six sides, and if we consider rolling two dices together, the number of probabilities increases. Assuming X is the random variable of getting the sum of the numbers of the two rolled dice.
X((n1, n2))=n1+ n2
Therefore, the probability mass function fx will be expressed as:
fx(S)=min(S-1, 13-S)36, for S{2,3,4,5,6,7,8,9,10,11,12}
MEAN OF RANDOM VARIABLE:
The mean of any random variable is termed the average value of a variable. The outcome of this average or mean random variable depends upon the probability of the result. In simple words, the mean of a random variable can be defined as the average of the expected value of random variables.
VARIANCE OF RANDOM VARIABLE:
The Variance of a random variable is the closeness of each value of variables to the mean of the overall random variables. It is considered that if the Variance of a random variable is of a small value, it is closer to the mean of a random variable. The Variance of a random variable is found by squaring each value and multiplying it with the probability given. Sup up this squared value of all the variables and subtract from the mean of a random variable. Considering X as the value of random variable p as probability and as the mean of random variables, then mathematically, the Variance of a random variable can be expressed as.
Var(S)=x2p-2
CONCLUSION:
The random variables are defined as the variables whose results are based upon random experiments, and the future value of those variables is unpredictable. A random variable is categorised into two types, i.e., discrete random variables and continuous random variables based on probability. To better understand and clarify the concepts over the random variables, it is better to get a brief knowledge about the theory of probability.
