In this chapter we will be seeing what is the probability distribution? And how in statistics, the different probability distribution comes to work? Suppose I have 1x random variable which has more than one possible outcome.
If I repeat any experiment, n number of times and plot the probability of every possible outcome.
in that particular case the probability that I have plotted with regards to corresponding x that will be called as my probability distribution.
Like I have different values of x, 0, 1, 2, 3, 4.
And my probabilities corresponding to it are in this way, 0.067 when x is 0, 0.2 which x is 1.
In this same way different probabilities, we have represented in the form of a table.
If I draw this particular table in the graph form.
Where x equals the number of red balls which we had seen in the last example.
I'll take that in the x axis and I will take the probability on the y axis, after this the curve that I will get, it will be called the probability distribution curve.
We even call it a histogram.
And there are two properties which are called probability distribution.
There is no negative value in this particular case and the sum of all the probabilities add up to one.
So, what is the probability distribution? It is one such type of representation which is the probabilities for all the possible values of x.
Now what are the different types of probability distributions? Based on the data generated which means if I have generated any data, I have worked on any data and I have collected it.
On that basis I have 2 types of probability distributions.
First is discrete probability distribution, second is continuous probability distribution.
Discrete probability distributions are those distributions in which we see the probabilities of discrete random variables.
Now what is a discrete random variable? Discrete random variable means that any such random variable x which we were discussing right now, any x’s value which is finite and which we can count, means any such x in which my number of possible outcomes can be counted, we call that as discrete probability distribution.
Like we will take one example, if I have one coin and I have toasted it, I can get heads or tails on it.
So, the events that are there of heads or tails that will be called discrete random variables because nothing can come in between those.
Either it can be only heads or only tails.
One more example, number of students in any class, okay.
What is it in that particular case? We can count all those students, this is my one example of discrete probability distribution.
If I have rolled one dice, in that dice there is a possibility of getting one, two.
From one to six, there is a possibility of getting any number but we can never say that if I rolled the dice I'll get 1.5 or 2.45.
So, any such probability distribution in which we can see a finite or countable number of possible outcomes, that we call a discrete probability distribution.
They are of different types, discrete probability distributions.
In this chapter we will discuss Bernoulli distribution, Binomial distribution and poisson distribution.
Next comes the continuous probability distribution, continuous means, any such distribution whose all possible outcomes are in any continuous range which means we have to take such a value which is in a particular range, it can be finite or infinite.
Suppose I weighed a girl.
A girl’s weight can be any number.
It can be 54 kgs of 54.5 kgs as well.
If I see the height of any student in the class.
So, any kid can be 165 cm, any other kid can be 155 cm, other kids can be 154cm.
So, in this way when the values lie with me in a range, whether finite or infinite, that forms my continuous probability distribution.
Even these can be of different types.
In this we will discuss uniform distribution, normal distribution, log normal distribution and Exponential distribution.
We will see all these.
Now, I have probability distribution but I have to write it in general mathematical form with my probabilities of every outcome.
For that particular case we will make use of probability functions which means suppose I have discrete random variables, means I have such random variables which I can count whose quality but they are finite it can also add any particular random variable which I can count.
Whose probability of every particular outcome I can count and it is finite.
It can also be possible that any such random variable, which lies in a particular range.
So, to define these kinds of different functions we use probability functions.
If I talk about discrete distributions then we call it as a probability mass function.
If we are talking about continuous mass distribution then we call it as probability density function.
We will see about is going ahead.
PMF, Probability mass function and PDF, Probability density function, what is the difference between these two and how they're useful to us? One important thing, the total value of both PMF and PDF in any particular domain, that is always one.
This is a simple thing that my probability always sums up to 1.
In the same way probability density functions also comes to 1 after the summation.
So, in this chapter we saw that what are the different types of probability distribution.
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This course is really nice, just have one question in empirical rule explanation , SD deviation example trainer is saying mean however mean (20+30+40+50+60+70/6) value is different kindly confirm than