[Ezra Halleck]

Please dis­cuss con­cepts and ex­am­ples from prob­a­bil­ity as well as re­views of web­sites you have found in­ter­est­ing.

[Chand]

I looked at the site many-eyes.com, that site has alot of use­ful in­for­ma­tion about graphs and charts that we can cre­ate to show how our datas com­pare to one an­other. From the looks of it, it seems a bar graph is the best way to go. Mu­tu­ally ex­clu­sive means that there are two events but both can­not occur at the same time and con­di­tional means that two events can occur at the same time? Or that an event can occur even if one has al­ready oc­curred? Just cu­ri­ous.

Chan­dini P.

[Ezra Halleck]

Yes, mu­tu­ally ex­clu­sive means that there are two events but both can­not occur at the same time. From the point of set the­ory, each event is rep­re­sented by a set of out­comes. If the events are mu­tu­ally ex­clu­sive, then their in­ter­sec­tion is empty.

Con­di­tional means that you re­strict the set of out­comes under con­sid­er­a­tion to one event (the given) and then look at an­other event. In Jan­u­ary, P(snows | pre­cip­i­tates) is going to be higher than P(snows), since we are look­ing at a more re­stric­tive set (pre­cip­i­tates) but which con­tains the other set (snows). On the other hand P(clear skies | pre­cip­i­tates) is going to be smaller than P(clear skies). In fact the events “pre­cip­i­tates” and “clear skies” are mu­tu­ally ex­clu­sive.

One word of cau­tion re­gard­ing your last ques­tion, is that you should not think of events as nec­es­sar­ily hap­pen­ing in real time. In­stead, it is bet­ter to look at the sub­ject from the point of view of sets. How­ever, if an ex­per­i­ment has fin­ished and an out­come has been de­ter­mined, then that’s it, no new events can occur.

[Chand]

Thank you for ex­plain­ing that. Since the in­ter­sec­tion is empty, then A is shaded and B is shaded but noth­ing is com­mon (that’s how I will get the con­cept, lol). OK, so be­cause there’s clear skies that doesn’t mean it will pre­cip­i­tate. Also, on one of the ques­tions about tak­ing out a ball from an urn and then tak­ing out a sec­ond ball, with­out re­plac­ing. So say there are 10 balls, and you take the first one so it’s 1/10. Then you take a sec­ond so 2/9? Or would it be 1/9 and 2/8? Be­cause you are tak­ing out a ball so that leaves 9 and then you are tak­ing a sec­ond but you’re not putting in the first one there­fore only 8 balls are left. Am I get­ting the right con­cept here?

[anthonyng]

as i pre­pared for class today, i ac­ci­den­tally also read sec­tion 5.6, hy­per­ge­ometic ran­dom vari­ables. why was the sec­tion skipped over? not a use­ful ran­dom vari­able to un­der­stand?

[anthonyng]

why is the con­stant e used to com­pute pois­son ran­dom vari­ables and not some other con­stant?