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:

Improper Integrals:

Integration Into Inverse Trig:

Integration of Rational Functions:

Integral of Logarithmic Functions:

Integrating Exponential Functions:

Integration Formulas:

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Integration By Tables:

Reduction Formulas - Integration:

Center of Mass & Moments:

Center of Mass & Centroid Problems:

Hydrostatic Force Problems:

Probability Density Functions:

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Normal Distributions - Calculus:

Homogeneous Differential Equations:

1st Order Linear Differential Equations:

Bernoulli's Equation for Differential Equations:

Slope Fields:

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Converging & Diverging Sequences:

Monotonic & Bounded Sequences:

Calculus Final Exam and Video Playlists:

Full-Length Videos and Worksheets:

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[kenkinyua]

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[brucesmith]

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

[patrickmayer]

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

[georgesadler]

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 YouTube TV with the Organic Chemistry Tutor.

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

[jessjakubek]

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?

[ShieldAniekan]

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

[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

[kellyredds]

Hi. Please why did you integrate and then differentiate?

[francinevoltaireledesma]

Thank you, we practiced so much. Nice G

[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

[Alchemist]

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

[bharatsahijwani]

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

[aaronrappleyea]

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