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Data Analysis

Probability
Probability Theory
Random Variable
Continuous Random Variable

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Probability Theory
What do you mean by Probability
Probability is measure of occurance by which we can determine how likely a thing will occur or take place.
For example when you use a coin for toss what is probability of coming Head or Tail. In this case both have same probability i.e. 50%.

In mathmetically we represent probability as:

P(A) = (Total occurance of A / Total Possible Outcomes)

So in above example(tossing a coin) Head or tail can appear only once when we use the coin for toss. But total number of possible outcomes are 2, i.e. Head and Tail.

So we can measure the probability of Head as follows:
P(Head)=1/2=50%

1 Repersents how many time head can appear in a single toss, and 2 represents number of possible values from which a value can come in a single toss.

Few important things
If your sample outputs are grater(in above example only 2 head and tail), in that case each element or item (output) for that sample has less probability as compare to sample with less outputs. Less output Grater Probability, More output Less Probability.

0 <= P(A) >= 1 That means probability of A is always between zero and one, or it can be equal to zero or one.

If P(A) = 1 then we have only 1 output for that particular sample.

OR and AND

Suppose you are conducting a survey outside the supermarket and your target is to get answer from 250 peoples. Suppose your findings are given below.

120 Peoples buy soft drink.
30 Peoples buy milk
Assume: Those who buy milk not buy softdrink and those who buy soft drink not buy milk(Such situation is known as mutually exclusive).

Now if we individual probability is given below

P(SoftDrink)=120/250
P(Milk)=30/250

So we can calculate total probability of both events using following formula:

P(A OR B)=P(A)+P(B)

P(SoftDrink OR Milk)=( (P(SoftDrink) = 120/250) + (P(Milk) = 30/250) )

P(softDrink OR Milk) = 150/250

Note::We use "OR" only when there is nothing common between two probabilities, that's way in the above example we assumed people who buy softdrink not but milk and people who buy milk not buy softdrink.

Random Variable

In simple language random variable is variable that can hold quanititative value(Nominal, Ordinal, Interval). Value of random varibale may change. The change in value depends upon the probability rules.

Lets consider following example.
Suppose we have a dice, and we know only one value can appear out of six (1,2,3,4,5,6). Value is quantitative not qualitative.

Probability Distribution and Random Variable
Probability Distribution assign probability to each quantitative value that a random variable can have. In above example we have six different values that random variable can have. Probability Distributation for those values is given in the following table.

Values that random variable can have123456
Probility correspoding to the values1/61/61/61/61/61/6
In the above example we have same probability for each quantitative value, but in other situation we may have different probability for different quantitative values.

Probability

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