Set Notation in Probability: Clarifying the Meaning of Union and Intersection

Mesmer
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I'm having a little difficulty understaning the notation used in my probability class. Would someone tell me if I'm on the right track with it :)


A\cup B is the event "either A or B or both." Does this mean that A and B can happen together and that A or B can happen alone?


A\cap B is the event "both A and B" Does this mean that both events MUST happen?
 
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Mesmer said:
I'm having a little difficulty understaning the notation used in my probability class. Would someone tell me if I'm on the right track with it :)


A\cupB is the event "either A or B or both." Does this mean that A and B can happen together and that A or B can happen alone?
Yes, that is the "inclusive" or: A or B or both.

A\capB is the event "both A and B" Does this mean that both events MUST happen?
Yes.

Now I'm getting a message that my reply is too short! How long does it have to be?
 
10 characters :p
 
Gib Z said:
10 characters :p

...and it doesn't even include space bars! :-p
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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