Cumulative Distribution Function With Example || Lesson 46 || Probability & Statistics ||

Cumulative Distribution Function With Example
In this class, We discuss the Cumulative Distribution Function With an Example.
The reader should have prior knowledge of the probability distribution function. Click Here.
We take an example and understand the concept of the cumulative distribution function.
Example:
Toss three coins.
Random variable X = number of heads.
The below table shows the probability distribution for the random variable X.
f(x) is a function that provide the probability values for the random variable X = x.
Cumulative distribution function:
The name itself says cumulative. I.e. add the previous probability values.
The cumulative distribution function is shown as F(x).
F(x) = P(Xlt= x) = Σxi lt= x (fxi)
Important: You can write the cumulative distribution function if you know the probability mass function.
Example:
The below table shows the probability distribution for three coin tosses.
Find the cumulative distribution function.
F(x) = 0 if x lt 0
= 1/8 if 0 lt= x lt1
= 4/8 if 1 lt= x lt 2
= 7/8 if 2 lt= x lt 3
= 1 if 3 lt= x lt infinite
Similarly, we can convert the cumulative distribution function to the probability mass function.
Example:
The cumulative distribution function F(x)
= 0 if x lt -2
= 0.2 if -2 lt= x lt 0
= 0.7 if 0 lt= x lt 2
= 1 if 2lt= x
Solution:
f(x1) = f(-2) = 0.2
Our first random variable value X = -2
Second random variable value X = 0
f(x1) + f(x2) = f(-2) + f(0) = 0.7
f(0) = 0.7 – 0.2 = 0.5
Third random variable value X = 2
f(x1) + f(x2) + f(x3) = 1
f(-2) + f(0) + f( 2) = 1
f(2) = 1 – 0.7
f(2) = 0.3
The below table shows the probability distribution for the cumulative distribution function F(x).

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[Geetha-Pitta]

bro ....since so many days i have been watching hindi lectures....watching in southern slang feels homely😁😂

[myofficial]

Best explanation ever.
Hats off you sir ☺️

[dhanushreeyadav]

very nice and understanding concept very easy way ..thank u for ur wonderful explanation

[Taniya-xrev]

You explained in simple way
Awesome lecture

[frozenhotdog-tolg]

understands this better than my university professor. It's not that he's dumb in teaching whatsoever. Its more like personal preference

[kushkapadia]

Thank you for teaching the subject fundamentally.

[saurabh]

if 2 <= x <= 3, in this case we take the values less than three but we should also take values greater than 2, then why we are not only taking the vlaues in between 2 and 3 ??

[myofficial]

Please carry on. Very soon you will get popularity.👍👍🏻

[pruthviprasad]

wow awesome explanation sir. thank you so much

[aiswarya.v]

0<x1<x2<2 how to solve this type of questions

[madhurjyapathak]

Thank you so much sir for such good explaination

[saudasad]

Sir use some Hindi language
Tomorrow is my board exam of maths

[aadityagoswami]

Sir 1 mistake that you have done frequently is you was calling the function x greater than equal to 0 and less than 1 as x less than equal to 0 and less than 1!!
It was your blunder mistake

[ekinozalp]

abi çok iyianlatıyosun da arada neden bıkmışsın ve bize kızıyomuşsun gibi geliyor çok üzüldüm

[blacksugar]

at 3:48 it is not sigma it is summation

[suneelramireddy]

I would give u 1000 likes if I could ❤