Continuous Probability Distributions - Basic Introduction

This statistics video tutorial provides a basic introduction into continuous probability distributions. It discusses the normal distribution, uniform distribution, and the exponential distribution. The probability is equal to the area under the curve and the total area under the curve is equal to 1. This video gives you some formulas that you might find helpful. It also briefly discusses the difference between continuous random variables and discrete random variables.
Probability - Free Formula Sheet:
bit.ly/3zb22rW
Statistics - Video Lessons:
www.video-tuto...
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Introduction to Probability:
• Introduction to Probab...
Probability Formulas:
• Probability Formulas, ...
Probability Explained:
• Probability Explained!
Probability With Geometry:
• Probability With Geome...
Probability of Complementary Events:
• Probability of Complem...
Conditional Probability:
• Conditional Probabilit...
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Independent and Dependent Events:
• Probability - Independ...
Probability of Mutual Exclusive Events:
• Probability of Mutuall...
Multiplication and Addition Rule:
• Multiplication & Addit...
Compound Probability:
• Compound Probability o...
Expected Value:
• How To Calculate Expec...
Probability Tree Diagrams:
• Probability Tree Diagrams
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Bayes Theorem:
• Bayes' Theorem of Prob...
Probability - Binomial Distribution:
• Finding The Probabilit...
Probability - Geometric Distribution:
• Geometric Distribution...
Probability - Poisson Distribution:
• Introduction to Poisso...
Continuous Probability Distributions:
• Continuous Probability...
Probability Density Functions:
• Cumulative Distributio...
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Probability - Uniform Distributions:
• Continuous Probability...
Probability - Exponential Distributions:
• Probability Exponentia...
Probability - Normal Distributions (Calculus):
• Normal Distribution & ...
Probability - Standard Normal Distributions:
• Standard Normal Distri...
Probability - The Law of Large Numbers:
• Law of Large Numbers
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Final Exams and Video Playlists:
www.video-tuto...

[@TheOrganicChemistryTutor]

Probability - Free Formula Sheet: bit.ly/3zb22rW Statistics - Video Lessons: www.video-tutor.net/statistic.html

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[@preciousmaelane274]

Why do we divide the standard deviation of a uniform distribution with square root of 12??

[@pganesh8318]

That's the formula You can check the derivation on the net if you are too curious about it

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Could you please make a video about eigenvalues and eigenvectors ?

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[@JackyVSO]

I'd love to understand why these formulas apply to the exponential distribution

[@sirgreen2792]

7:52 why 12? for when we are finding the standard deviation

[@EssyEssitah]

My question too???

[@edmea658]

@@EssyEssitahI want to know too

[@tajourahmedsaif1731]

The number twelve comes from the mathematical derivation of the variance formula for a uniform distribution. Without diving too deeply into the calculus, here's the intuition: 1. Variance measures how spread out the values are from the mean. 2. For a uniform distribution, the spread is symmetric and depends on the square of the range ((𝑏−𝑎)2). 3. The 12 appears as a result of integrating the squared deviations over the uniform interval and dividing by the range. It ensures the variance formula is mathematically consistent. The 12 is essentially a scaling factor that normalizes the spread for a uniform distribution. It arises naturally from the derivation and reflects the even spread of values over the interval.

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Thanks

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Sir , can you pls make a KZbin class on multinomial distribution ( the mean and the variance ) to be precise. Thank you sir

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What software does he use to write on the black background ?

[@TruthNerds]

(Unsurprisingly,) you only cover absolutely continuous distributions. The other principal type of continuous distribution, singular distributions, is not even mentioned. To be honest, they are a mathematical curiosity and I've only heard of them myself today. 😄 But now it appears to me that starting with continuous distributions in general first, i.e. the distribution function, and then going from there to absolutely continuous distributions (such that the derivative is the probability density function) arguably makes more sense didactically than starting with the density function and using integral calculus to then explain distribution functions. For instance, if you start with the distribution function F(x), then P(x ∈ [a,b]) = F(b) - F(a), which is simpler (and more general) than the integral approach (area under the curve).

[@vigneshwarvijayaraj9689]

Uniform distribution is a type of discrete distribution right? Correct me if I am wrong

[@matthewthompson6455]

Yes correct, there’s a continuous one and a discrete uniform distribution

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Hold up. So if Lambda and the Mu sign are interchangeable to represent mean. Does it mean i can also write Mu=1/Lamda

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looking for the playlist but can not find it

[@superstarwarrior2933]

Standard deviation is ((b-a)^2)/12

[@roberte.6892]

W/ respect to the exponential distribution, what is "e"?

[@dialglex]

"e" is Euler's number, which is a mathematical constant approximately equal to 2.71828

[@madhusudanthore773]

What is mean formula in exponential distribution

[@mattrhoades9487]

Surprised you didn't sneak in the standard deviation of the exponential distribution is equal to the mean of the distribution.

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Can someone help me on his algebra1,2,3 playlist. I don't think if it's in the proper order. I'm trying not to miss any of the topics.

[@TheCivilizedCaveman]

but how do you calculate the area under the curve??? 2:08

[@matthewthompson6455]

Integral baby

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I'm here because my lecturer is too lazy to explain this topic using his own voice and instead, he used robot's voice which make me hard to understand

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i have exam this week and i watched 3 times and i didnot understand anything

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Julio Gonzales

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bell curve's sus

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Thank you