Mean & Variance of the Exponential

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MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
Instructor: Jagdish Ramakrishnan

License: Creative Commons BY-NC-SA
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For me, it is more intuitive to find P(min(X1, X2) <= w) through event P(X1 <= w or X2 <=w):
P(X1 <= w or X2 <=w) = P(X1 <= w) + P(X2 <= w) - P(X1 <= w and X2 <=w) = P(X1 <= w) + P(X2 <= w) - P(X1 <= w)P(X2 <= w)

mikhailkilianovski
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That was a really informative video. I felt like I just reviewed my calculus math.

ShinCharles
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why isP[ max(x1, x2, x3)] equivalent to P[x1<=z & x2 <= z & x3 <= z]? lets label the first equation as 1(P[max(x1, x2, x3)]) and second as 2. in 2 we are actually putting a stronger constraint than equation 1, so equation 2 is a special case of 1, but not necessarily true that 2 has to happen. So why are taking equivalence?

randalllionelkharkrang
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Thanks. It's very helpful reviewing the calculus thing!

MinhNguyen-ggiu
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this is perfection . greet explaining keep it up

عبداللهاللهيب
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why did t turn into negative t suddenly ? where did the negative appear for the -e from ?

worstyearever
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can we just use theta for the mean. lol why are we making it harder than it needs to be

jonahberrong
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where is the lamda in integer of variance? wkwkwk :D

footballonfire
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Good example there but the board was reflecting a lot of light, I strained a lot while following the tutorial

AmbroseOdhiambo
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can you calculate lamda out? by integrating fx from 0 to infinity

lijerry