Random Experiment:
The processes for which outcomes cannot be predicted; like flipping a coin, rolling a dice, picking a card from a deck of cards , Measuring heights of students , Taking data of temperature for one month for analysis etc.
Random Variables
A variable that will take a value assigned to it by the outcome of a random experiment .Commonly denoted as ‘X’ (Capital X)
Realization of a random variable:
The outcome of the experiment after it occurs. The value that is assigned to the random variable is the realization. Commonly denoted as ‘x’ (small x)
X = the variable, x = the outcome
There are two types of Variables
- Discrete
- Continuous
Discrete –
When the value of the variable is given in the integer form (not in decimal), is known as Discrete Variable. Like 1,2,3,4 ,5 …………e.g. flipping coin, picking a ball from a box, rolling a dice , all these measurements cannot be in decimal form means we cannot say there is 1.2 head after tossing a coin or after rolling a dice we get 3.5 .
Continuous –
When the value of the variable is given in the decimal form, is known as Continuous Variable. e.g. Weight of anything , Distance , Temperature etc.
Range of Random Variables –
The set of possible values of a random variable is known as range of random variable.
Probability Distribution
The probability of the values in the range is known as Probability Distribution. Commonly denoted as P(X = x).
Uniform Probability Distribution
When all the values of random values occur with equal probability is known as uniform probability distribution, like; after flipping a coin there are only two possible outcomes one is head and another is tail. Each possible outcome is a random variable (X) and there is equal chance of getting either head or tail so P(X) = 1/2.
Similarly in a deck of cards there are 52 cards, so total possible outcomes 52 for any card from this deck and each outcome is ‘X’. Now the probability of picking an ace of spade is
P (X) = 1/52.