Probability Density Functions

This calculus 2 video tutorial provides a basic introduction into probability density functions. It explains how to find the probability that a continuous random variable such as x in somewhere between two values by evaluating the definite integral from a to b. The probability is equivalent to the area under the curve. This video also contains an example problem with an exponential density function involving the mean u which represents the average wait time for a customer in the example problem.
Probability Formula Sheet:
bit.ly/3zb22rW
Improper Integrals:
• Improper Integrals - C...
Integration Into Inverse Trig:
• Integration into Inver...
Integration of Rational Functions:
• Integration of Rationa...
Integral of Logarithmic Functions:
• Integral of Logarithmi...
Integrating Exponential Functions:
• Integrating Exponentia...
Integration Formulas:
• Integration Formulas F...
________________________________
Integration By Tables:
• Integration By Tables
Reduction Formulas - Integration:
• Reduction Formulas For...
Center of Mass & Moments:
• Moment, Center of Mass...
Center of Mass & Centroid Problems:
• Center of Mass & Centr...
Hydrostatic Force Problems:
• Hydrostatic Force Prob...
Probability Density Functions:
• Probability Density Fu...
_________________________________
Normal Distributions - Calculus:
• Normal Distribution & ...
Homogeneous Differential Equations:
• Homogeneous Differenti...
1st Order Linear Differential Equations:
• First Order Linear Dif...
Bernoulli's Equation for Differential Equations:
• Bernoulli's Equation F...
Slope Fields:
• Slope Fields | Calculus
___________________________________
Converging & Diverging Sequences:
• Converging and Divergi...
Monotonic & Bounded Sequences:
• Monotonic Sequences an...
Calculus Final Exam and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Probability Formula Sheet: bit.ly/3zb22rW Final Exams and Video Playlists: www.video-tutor.net/ Next Video: kzbin.info/www/bejne/nXmlfWiQltpmhKc

[@braingump2345]

Using this for my 50 percent exam 😢

[@priv.dm9]

My 60%💔

[@tumuyangen7172]

😢😢😢

[@nataliarobinson5671]

I have been using your channel since GCSE and now I am still using it in university - thank you for all your help!!!

[@ophiliasantos785]

Your speech is so clear. I like your channel than many others. God bless you

[@mohamedabubakar8487]

we need face reveal, sir.

[@Test-ri2kr]

@Billy Ronan no it didn’t dude shut up

[@arisoda]

why do indians always say "sir" on the internet lmao

[@polarisalpine2638]

@@arisoda it's just respectful y'know-

[@arisoda]

@@polarisalpine2638 except everyone finds it annoying

[@polarisalpine2638]

@@arisoda that's them, I honestly find it very respectful, and it also varies upon the person I'm confronting, if they don't have any problems with someone saying them "sir" then I think it's fine, ofcourse I'll appreciate if someone called me "sir" but that's just me-

[@542395633]

0:23 equal to or LESS than zero you said? But the sign is equal or bigger than zero?

[@ahmedfathi5448]

Thank you bro so much your content is phenomenal, you’re a lifesaver man keep up and always provide us with something new 👍🏻

[@lizzaliz]

You've saved my life more times than I can count. Keep shining, thank you!

[@patrickmayer9218]

Personal note for calc 2, don't worry about exponential density, just worry about the ones like the first problem.

[@brucesmith9726]

For anyone asking, he plugs the definite integral evaluated from 4 to 5 into a "definite integral calculator" symbolab works

[@jessjakubek3184]

What are you putting into the calculator at 4:40 ? Are you just following the same process but without having to work out the common denominator?

[@DarthAsthmatic]

I get sooooo relieved when I find a TOCT video on a topic I need to understand

[@nomad2458]

You deserve a Nobel peace prize. Thank you 🙏🏿

[@francinevoltaireledesma7996]

This is probably 3 years too late but, what did you put at 4:28 in the calculator?

[@ayze6095]

I am wondering as well

[@TheFightFlash]

I was quite confused with the sign here 0:27, you said it has to be eq. or less than zero, but you wrote it as greater than or eq. to zero

[@AshutoshKumar-ij6ty]

it was a mistake, he corrects it by saying it can't be negative

[@leroystudent3024]

He's so fast! Why are you going so fast? I'm watching at x0.50 and still cannot catch up with you.

[@Super_Sayan_Broley]

Sir, I did not understand how did you derive a function for 2nd problem (the waiting time one), I mean how did you get that (1/U*e^-t/U)? apologies for my dumb question in advance

[@mod2]

That's just the formula of the exponential density function (usually represented using lambda). Here he has replaced lambda with 1/t. He. hasn't derived it here, but you can probably find the derivation on Google or some other KZbin video.

[@kellyredds7292]

Hi. Please why did you integrate and then differentiate?

[@dempsey3810]

Ach, another video completely detached from the reality to which PDFs are applied. Gosh, that's why so many run away from maths because maths are never empirically taught. Next.

[@aaronrappleyea8202]

so why is the greater than 4 not evaluated differently in the integral?

[@zebruhmlz8801]

in my head i feel like it shouldnt matter whether its inclusive but i could be wrong.

[@gobbergobberer4776]

@@zebruhmlz8801 I think you're right. The probability that a continuous density function is a constant is always zero. P(X=c)=0

[@kameronbriggs235]

Im not going to pretend to know where you pulled one over u times e to the negative t over u power from.... lol

[@navjotsingh2251]

It’s just the definition of the exponential density. There are great videos on KZbin explaining it very well using formulas and explains how they work. Just quickly search and watch a few short videos and you’ll understand :)

[@vansf3433]

Calculus can be useful only when there is a boundary , and the upper bound band the lower bound are specific and definable values. Otherwise, it will be come a sort of nonsense -generating mathematical notion

[@kenkinyua7036]

this channel is the reason i ace my tests thanks so much

[@bradleyplummer5778]

at 0:21, you say "if its a PDF than it has to be equal to or less than zero..." Is that correct? or did you mean to say "greater than"?

[@ShieldAniekan]

Bro I love Ur Videos thank u so much for doing this

[@terrywayne_]

what are you plugging in the calculator?

[@ArchangleTyrel2]

1/e^(7/5)

[@wrjazziel]

Yeah I wonder the same!.... how did he get 10.4 and 54.4 percent from the calculator... :S

[@ayandaduarte.c1708]

Thank u sooo much😭❤️

[@jaypatel9221]

In question 1)B and C part was in calculator so please show how to do it !

[@JustinGreathouse-r4i]

Lee Karen Clark Robert Young Patricia

[@jeyko666]

I love your Brooklyn accent

[@bharatsahijwani441]

Very helpful sir thank you. Also I request you to cover binomial , poisson distribution , discrete distribution. Plz sir

[@valeriagoguv7302]

did he? im dying

[@i_mreed]

@@valeriagoguv7302 did he? im dying tooooo

[@wrjazziel]

Thank you so much!

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for an outstanding Introduction to the Probability Density Functions in Calculus Two. I also encountered Probability Density Functions in Engineering Physics Three and Engineering Probability, which is an Undergraduate required course in Electrical Engineering. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@ApurbaMandal420]

I think he meant that X must be equal to or greater than 0

[@allyknight6872]

I’ve got 30 minutes before my exam 🙏🏻

[@graceplumitallo1517]

how would you get the decimal without using a calculator

[@dzangam1879]

probability mass function ?, when will you do that ?

[@jaouadrahouani4975]

So can anyone explain? he mentioned " f has to be equal or less than zero" but wrote down f>=0.....

[@MrJeanmarc101]

He said it wrong but wrote it right. It has to always be over 0 because we are calculating a probability. By definition, probabilities can only have an image of (0,1). Hence, why a probability fonction can never be negative or over 1 for that matter.

[@Alchemist10241]

awesome - I reviewed a lot math by just solving these two problems. great job

[@KevinDhoundiyal]

how do you get 54.4% for part c in the first example, what numbers did you plug in?

[@jesicamarisikat724]

you get the anti-derivative of the f(x) first and then you plug in the limits from 1 to 3 to get 0.544 or 54.4%. he used a calculator

[@lydia7802]

I got 28.8%

[@zapper354]

Learning this to win in Battleship

[@talhazaigham3575]

I love you

[@gboladeaduragbemi4508]

Thanks for saving me

[@U2vl9v0]

4:27 why did I get .808

[@Hakuuu99]

THANK YOUUUU SOOO MUCH

[@onnysmenete2350]

hello, with calculator do you use?

[@francinevoltaireledesma7996]

Thank you, we practiced so much. Nice G

[@onepeopletv6531]

Thank you

[@ccbl6270]

thank you so much

[@chandrajyothibojjapu9566]

Thank you so much sir

[@rashidkalimbo2451]

thanks

[@johnhhu2137]

Thank you

[@tjosman7755]

I really love ur way of teaching sir

[@tanusharma854]

Superup sir🙏🙏🙏

[@vansf3433]

One of the biggest problems of nonsense in calculus is using such non-existent values as negative infinity and positive infinity as specific values to evaluate a sort of subjective mathemstical statement. That's where nonsensical formulas in physics come from .

[@mouhassan6117]

GOD Of Mathematics

[@mutalimichael]

There is only one God

[@vansf3433]

The area under a curve which extends to infinity can never be 1 as unbelievably ignorantly stated and copied by the ignorant

[@traiamadelyn7309]

His voice makes me sleepy

[@kaidothedragon2821]

why did you skip b wtf

[@MsLipsxLikeSugar]

Plssss plsss show on finance calculator Texas Instruments how to calculate definite integrals 🙏🏻