0:30 Summary of discrete probabilities and outcomes 2:06 Important axioms in probability 7:04 Measurement of probabilities 11:18 *Continuous Random Variables* 16:13 Important change when we go from discrete to continuous probabilities - the idea of probability densities 18:24 How to construct Probability Density Functions (PDF) 24:00 Example 1: PDF in physics 26:21 Example 2: Non-uniform distribution PDF in physics (Gaussian velocity distribution) 31:05 Mapping one distribution to another
I think he is confusing Prob. density with the overall Probability _ probabilitygenerically is the area under the curve which its total is always equal to 1 and at the mid point the area under the curve is actually HALF
@21:58 i don't think it should saturate to 1 at +ve infinity it should be a gaussian function or even a constant function because the variable can lie between -inf to +inf so the distribution is exactly half saturating to 1 or 0 means finding the variable there is highly possible or highly unlikely which is not the case here
GMN Come on, bro. It’s not about being precise. This is something we start learning in set theory in our school. And after spending so many years in science, this is something that comes automatically.
0:30 Summary of discrete probabilities and outcomes
2:06 Important axioms in probability
7:04 Measurement of probabilities
11:18 *Continuous Random Variables*
16:13 Important change when we go from discrete to continuous probabilities - the idea of probability densities
18:24 How to construct Probability Density Functions (PDF)
24:00 Example 1: PDF in physics
26:21 Example 2: Non-uniform distribution PDF in physics (Gaussian velocity distribution)
31:05 Mapping one distribution to another
Thanks again 😅
@21:40 the CPF dosen't need to be half only at 0 right it could be anywhere .... Depends on how we define the random variable right !!
Like I define a new random variable Y=X-1 now 1/2 is not at 0 but at "+1"
Like I define a new random variable Y=X-1 So now 1/2 is at 1
I think he is confusing Prob. density with the overall Probability _ probabilitygenerically is the area under the curve which its total is always equal to 1 and at the mid point the area under the curve is actually HALF
its 1/2 at 0 because there are equal numbers at both side of zero.
Thanks
@21:58 i don't think it should saturate to 1 at +ve infinity it should be a gaussian function or even a constant function because the variable can lie between -inf to +inf so the distribution is exactly half
saturating to 1 or 0 means finding the variable there is highly possible or highly unlikely which is not the case here
You're not taking into account that it's cumulative.
@19:52 Did you really put a square bracket with infinity? Damn!
He is not being precise in his notation I think.
GMN Come on, bro. It’s not about being precise. This is something we start learning in set theory in our school. And after spending so many years in science, this is something that comes automatically.
@@sidddddddddddddd Yeah true. Just watch his lectures. It kind of feels like he come without any preparation. It is really sad.
He's a physicist, not a mathematician lol
@@ianz.0 Still *heaps* better than some of my teachers...