Let us start today’s topic on uniform probability distribution (I will discuss on continuous dist today).

Now, the concept comes in two forms: discrete and continuous. If I toss a coin then there are two possible outcomes: Head and Tail. If I roll a die, then it always return a digit (1 or 2or 3or4 or 5 or 6).

There is no number in between. That means the probability for tossing a coin is 1/2.

And probability for rolling a Die: 1/6

Now, if the random variable is continuous in nature like height, temperature etc.

There is always a number with some decimal points like height of a man: 5.565ft or temperature of the area: 12.43387℃.

So there are infinite number of chance to return the outcomes.

Now the probability of any outcome for continuous variable: 1/infinity = zero!

So what we can conclude? We cannot go for normal probability theorem which is used in discrete nature for a continuous variable. Then how can we calculate the probability?

Any guess? OK, let me tell you.. the way to calculate the probability is by some range .. that means; what is the probability of a man who has height 5.75ft?

Wrong question!

The right question is: what is the probability of a man having height between 4ft and 5ft.

How to calculate? We have a function named cumulative distribution function or CDF.

Proabililty of having height between 4 and 5ft =

-infinity < p(5) < 5

Minus

-infinity < p(4) <4

Now think.. we will get the area between these probabilities by subtracting them and that is the output of our question.

We can use cumulative distribution function or we can go for the standard z table chart to get quick answer for any kind of probability funding problem for continuous variable.

So what did we learn till now ?

In normal distribution, the probability cannot be calculated by PDF (probability distribution function) because as it is concept of continuous distribution, it always being calculated by a range that means difference between PDF of lower to upper range. That is the main concept of CDF (cumulative distribution function) but in binomial distribution function the pmf (probability mass function) is actual probability because it always consider a discrete sense of a single value, not any range.