Reply to queries

[Aritra Mandal]

Hello learners,

I am Aritra Mandal, your TA. I have tried to address all the queries. 

Please go through the following. Feel free to reply if there is any doubt.

Question 1>  I have a question about what is happening in this video at 00:05:09 -

http://www.youtube.com/watch?v=BGXmy4vA0R0#t=309s.

Why range of X is interpreted as subset of (mean-SD,mean+SD) but not as (mean-k*SD, mean*K+SD) for some k in R? Like why we assume k to be 1? That I have not understood. Please clarify this..

Answer> We are taking k=1 because 'mu' is the standard deviation. Interpretation of "Standard" forces us to interpret range of X as a subset of (mean-SD,mean+SD).

Question 2> I have doubt that why can't we use absolute deviation for which we can define variance as Var[X]=(E[ |X-E[X]| )^2 and thus AD[X]= sqrt(variance) = E[ |X-E[X]| ]. In that case also the problem of cancelling of errors is not there as we are taking their absolute values. 

I don't understand though it follows the same properties as that of rms SD, why the absolute deviation is not used in determing the spread of random variables. Also it is easier to calculate.    

I have this doubt for a long time but don't get any satisfactory answer yet. Please help in clarifying the doubt.    

Answer> Absolute deviation is also used in many analysis. It is not that people do not use it. Standard Deviation is more popular. Both of these deviations have their own pros and cons.

Question 3> At 21:20, we have found the probability of (S_n-mean)/sd to lie between a and b where a<b. I have attached the screenshort of the problem because with plain text it is difficult to write the integrals etc.   

I think I have created some mess during the derivation. Please clarify it.  

Answer> Your answer is not dependent on 'n', as you are taking limit n goes to infinity.

Thanks and Regards

[Himanshu]

@Aritra mam, thanks for the reply.   

In answer to question 2, you have written that "Both of these deviations have their own pros and cons".   

Mam may you please discuss the pros and cons of standard and absolute deviation? I want to know that.  

Thanks!