Probability Density Functions / Continuous Random Variables

[JayBlueToYou]

You do statistics too? this is magic.

[lowdihigh]

how do you actually determine what the probability distribution function is? I know you set up an exponential function for time, but I'm confused as to how you went about determining that, because on some of the questions that my professor gives me, he asks me to determine the pdf.

[DJAnthonyillWill]

Without PatrickJMT, there would be an increase in school violence lol. J/K Had to make another funny comment.

[jwb4291]

I have a probability professor with a SUPER thick accent making learning some of these key concepts rather difficult. I am an avid viewer of your videos and they help immensely.

[Chaminade14]

I should be paying you my university tution... just amazing

[patrickJMT]

@Chaminade14 donations available on my website. do not send all your tuition though, i can not grant you that worthless piece of paper you will get at the end!

[Chaminade14]

@patrickJMT I agree with you, most of them are useless, heck they give out degrees in basketweaving nowadays. However, act sci is one of the more useful ones out there ;) One can acutally turn that degree into cold hard cash =)

[jclwhite]

@patrickJMT It deserves to be worthless, but unfortunately, its required to prove what, potentially, can fit in your head. If it were worthless I would quit the maths modules I dislike studying right now!

[ahmedpharoah]

OMG it's like you cover EVERY heading in my calculus book! I love you!!

[pjfs80]

big thanks, I'm going back to th classroom after 9 years, 5 in the IT industry and my Master's degree is very math heavy, so I'm refreshing and quickly picking up related math. Probability is an important area for my course in Machine Learning, FYI.

[radhakrish80]

Excellent videos. I have started going to class all over again @53

[godling2007]

Not justifying, not justifying, not justifying........ You spend so much time talking about extra stuff rather than focusing on the problem itself. Do you really think people don't understand that the stated facts are basically valid for the context of the problem only, and perhaps modelling in real life would be much different? Don't get me wrong, I do hugely appreciate the time and effort you take to share these videos with us, but there is too much extraneous talk and distractions.

[Ameliadams]

@godling2007 for a person that needs detailed explanation to understand something, i had appreciate what patrick had done..makes me understand better

[patrickJMT]

@godling2007 dont watch. better yet, make your own far superior videos and do the world a favor. otherwise, you are just being another internet troll.

[LavenderBlossom1]

Your videos are amazing! Thank you so much =)

[SuperJane99]

this isn't as clear and simple as your other videos. I love your videos though they are wonderful and helping me very much thank you thank you thank you.

[mookieoftheshire]

Thank you for some beautiful examples with simple explanations. I wish you were my teacher for this semester.

[aadesh7]

Dear Patrick,

I am having some trouble with density function of a function of a random variable. The stuff which involves method of distributions functions and the method of transformations. Can you post a tutorial video for that? Thanks a ton for all your help! :)



[BUZZIEBEE]

You sir, you noble king amongst men, have NO idea how useful you have been to me throughout my university career so far. A thousand thank yous are not enough.

[themrinsig]

My question is somewhat related because it has to deal with Probability and I didn't know how to reach you. CAn you do a video on the sums and products of random variables?

[rinwhr]

3:19

Patrick you had t < 0, how could time be negative?

[bigk22]

@rinwhr the time cant be negative, that is why in the brackets to the left it says that the chance of t<0 is 0 as in impossible

[Aban0ob]

@rinwhr He set the conditions for the integral so that if time was negative, the probability would be 0. This means that, assuming a caller could wait for less than a time of 0 units, the chances of this occurring would be 0, or impossible.

[naveregnide]

Thanks a lot for this. It helped clear some things up.

[gabrielfinol]

more random variables!! pmfs too please!

[StealTeal]

Could you do a video w/ pdf and finding a conditional probability? Like "Find P(Y <= k | Y <= l)"? THANKS

[smokesidized]

If i may make a suggestion:

I think that you do an absolutely fantastic job explaining your steps and how to approach the problem, i think you would be able to fit in a lot more examples for people to follow if you only show how to set up the problem, it should be assumed that we all know how to do integration using u-sub and what-not

Of course detail will be required where needed, but hey, theres my 5 cents on the suggestions :)

Anyways, keep up the excellent tutorials :)

[imranbug81]

i m searching for a video which explains how do computer generate random numbers... ! is this video i should be watching... or is it just about probability certainty etc.. etc..... ! ??

[patrickJMT]

@imranbug81 well this is clearly not the video you are looking for.

[Danellos]

@imranbug81 Actually, what computers do is very interesting. You see, a computer cannot initially generate a random number on its own because it can't make its own decisions. However, most programming languages have a built-in function which takes in what one calls a "seed" when you attempt to generate a random number. This seed is taken in from the date and time of the computer, which changes with each passing nanosecond. Some calculations are done, and poof! Random number is generated :)

[djutopic]

Awesome explanation! Simple and straight to the point :)

[lolcore2]

PatrickJMT. You are god. I learn more from your 8 minute videos than any of my peers do in an hour and fifteen minutes of class.

[zanekirk]

I think you should commit to your ending statement and make more videos regarding random variables/processes. As you well know, you skimmed a snowflake from the iceberg. It helps that you are easily understood. Thanks for your time and effort in posting these videos.

[Wuzimu4444]

You are my hero. T_T

[dnallor24]

what grade is this based on. Im a junior will this help me



[Mrs1Me1]

Thank you so much :)



[vm299vm]

Absolutely love your videos. They are a big help. Would you be able to add more videos about the joint probability density function and how it is calculated for the normal, the poison, and gamma distributions? These are really hard topics to digest and I just have not seen much good material on this.

[kstatics]

so very clear. finally, i got the intuition. Love the way the set aside the justification of exp() part for the time being so that i could understand the use of pdf. thanks mate.

[TheAcehd]

you make it possible for me not to go to class :- D

[patrickJMT]

@TheAcehd go to class

[jormoria]

@patrickJMT will you please do brownian motion,I really want to learn ITO LEMMA,ITOcalculus and weiner process

[SourPeach]

PatrickJMT is the guardian angel of math students sent down from the heavens to guard us from the evil of math department academics! I need a picture of this man so i can sculpt him and put him on a crucifix... start a new religion

PATRICIANS! :D

skipped integral calculus, differential calculus, statistics for 1 semester.

start studying 12am night before 9am exam

watch patrickjmt

pass exam

get credit in differential calculus

EPIC WIN!

did not open my books. 0 lectures 0 tutorials.

[SourPeach]

@SourPeach have exam in 7 hours

souped up on caffeine & nicotine...

I WANT YOUR BABIES :D

[TheAcehd]

@SourPeach this is true

[Econ1260MetZRoberto]

@TheAcehd Owned! LMAO Go and get them!

[rycecorl]

Thanks a lot! this will help me for my exams!! :D

[ELZOOL12]

I learned something very important today thanks to your helpful video... Thanks a lot

[onaygizemgs]

omg it really helped. i have sac tomorrow on this topic and it was the biggest nightmare for me. thanks for the video :)

[fascist27]

MAY ALLAH BLESS YOU

[blackstars56]

@fascist27 wtf? dude not everyone is a muslim. idiot.

[NinjaVampirate]

Awesome, I missed this in school because I was ill the last week we were in, and now we're off for 2 weeks I don't really have anyone to ask so this helps a lot. Thanks.

[jeannepike]

patrickJMT

You are a godsend!

What a blessing to run into a talented instructor! Thanks!

Stay blessed, K?

Jeanne Pike

[shalnpaw]

wow, thank you so much, this video was extremely clear and concise. so helpful! dont stop!

[xxxcoolboyxxx]

patrick is the reason i dont go to lecture, so i can read the book and watch these videos and be set!

[scout6686]

@xxxcoolboyxxx

your too cool

what is your major?

[xxxcoolboyxxx]

thank you.. you are cool too lol

my major is electrical engineering =P

[xBTTN]

is this university work?

im doing this in college, i live in the UK.

my exams in 2 weeks and im really scared. CRV is SO HARD

[thomaskim599]

lifesaver/grade saver,

i don't understand why my profs aren't as simple.

[mahlerite]

Good teaching, like usual.

I want to add that there is an efficient technique that enables one to bypass the calculus altogether. Namely, knowing the cumulative distribution function (c.d.f.) of the exponential distribution allows one to simply plug in a couple of values into an equation and solve.

CONTINUED . . .

[mahlerite]

. . . CONTINUED

This particular c.d.f. is given by F(x) = P(X ≤ x) = 1 - e^(-λx), where x denotes the upper bound of integration and 1/λ represents the expected value of X, which is 6 in this case. Therefore, plugging in 2 for x and 1/6 for λ gives 28.3%.

[methushael]

thanks for this! i wish you could do transformation of random variables next

[akira4489]

i second that!

[shiskalashika]

How would you find constant c in a function i.e f(x)=cx^2 that lies at 0<x<3

[terrywoodinc]

thank you! I'm starting to understand, but i still find it hard to understand what kind o formula to apply given a problem set. Any way I can ind some kind of table that tells me what probability/distribution is associated to different situations? Or should i just practise a lot?!

[rappstack]

THANKYOU. i have a test soon and continuous random variables is really difficult to me.

[Shrubbs]

My final is tomorrow, so it's the end of Calculus forever (for me at least) but when do you set the integral equal to 1 and solve for k...and the mean (mu)? To find the mean, do you just multiply the function by X and then integrate?

[dasboot356]

Got some problems with that. The function is not scaled, this means the area under the density-function is not equal 1. Furthermore t have to be squared in the exponent. If not, you do not get a bell-curve! And if you put the square on the t, you never can intergate that. You have to look at a special table to determine this!

[patrickJMT]

you are very confused.

you seem to have normal curves on your brain for some reason.

this has nothing to do with the normal curve.

[dasboot356]

Okay, if this is not normal distributed you are right and the area under the whole curve is also one. And yes, I had the normal curve in my mind... but only because your function havn´t even a maximum at t= 6 min. (I plotted it) Could you explain this? Or am I competely wrong?

[Souliee]

This feels like great preperation for my upcomming class in propability theory and statistics! Thank you Patrick.

[patrickJMT]

my pleasure : )

[MrRiemannCalculator]

W00t!

[trese0000]

This was very interesting to know how math gets applied to life situations. Its better to learn about math this way.. Makes you more attentive.

[friendlyfire53]

The formula looks similar to the wave function in quantum physics.

[xb0xher0]

Is this like calculus or something?

[patrickJMT]

well, it uses calculus, but most would lump it in the area or 'probability' which is quite vast!

[dannystud]

perfect timing. i have an exam next wed on these.