Now, we will see different types of continuous probability distribution.
In this first comes uniform distribution.
Uniform distribution is one of the simplest probability distributions in statistics.
This probability distribution is such kind of a distribution in which every value in any interval between A to B comes equally likely, which means if I have an interval between a and b then the chance of each value coming up in the distribution is the same.
We call it a uniform distribution.
In this interval A is my minimum value and B is my maximum value.
Lets see its probability distribution function, what is its formula.
This is given as 1/b-a where my x’s value lies between the interval from a to b and in the remaining values it is zero.
Like we can see in this graph, where my values lie between A and B in that the probability of each point coming up is the same or is uniform.
So, we call this particular case a uniform distribution and this is widely used in distribution in our stats.
Now, let's see its examples, which all scenarios follow uniform distribution.
Suppose, I have rolled one dice, to roll that dice I have six possible outcomes.
Either 1 can come, 2 can come 3, 4, 5, 6 and you will see that the probability of every number coming up is the same, which is 1/6.
So, in this way, rolling a dice is an example of uniform distribution.
Now, if I pull one card from the deck of cards, in that the possibility of me pulling out a spade, even that is ¼, the possibility of me pulling out a heart card is also ¼.
The possibility of pulling out a club card is also ¼ and the possibility of pulling out a diamond card is also 1/4.
So, because of this reason, the possibility of pulling out a card would be a uniform distribution.
Let's take one more very easy example.
Suppose I want to guess somebody's birthday for the entire year.
We have in total 365 days in one year and I have to find which are the people whose birthday falls on 1st of January.
Now, it can be 1st January or 3rd January or 5th March, the probability of birthday falling on
any of the days is the same, 1/365.
Why? Because 365 is my total number of days.
So, these types of different distributions are found by uniform distribution.
And we use this widely in day-to-day life.
We'll see its mean and variance formula.
My mean is defined by a+b/2.
Why? Because my minimum value is a and maximum value is b in one interval.
And if I see its centre, it will be defined by a+b/2.
Variance formula is b-a whole square divided by 12.
We are not seeing its derivation.
But this is very easy.
You can put the values in the normal formula.
You will get the variance.
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