1062) HINT :
AM = \frac{\sum_{t=1}^{n-r+1}{\;\; \; t*^{n-t}C_{r-1}}}{\sum_{t=1}^{n-r+1}{\;\; \; ^{n-t}C_{r-1}}}
1) Suppose that x1,x2....xn are reals.
Given xi=-xn-i+1
S=ΣΣΣxixjxk summation is over all distinct i,j,k belonging to [1,n]
Find S.
2) Consider the smallest number in each of the subsets of size r of the set X={1,2,3,4,5....n}.
Show the arithmetic mean of the nos. so obtained is n+1r+1.
-
UP 0 DOWN 0 0 5
5 Answers
106
62raja .. is the answer to the 1st question independent of xi's?
I find it a bit strange (this question)
In the second question.. all you have to do is to find the number of subsets whose smallest element is r.. and then sum up :)
1@ nishant sir, there are options....and all the 3 options are in terms of n only.....with d) reading NOT.
2) Pls evaluate it...dat's the dbt, I'm a bit weak in bio summations.
1357take all the xi's as very close to zero but distinct..
The sum will be zero..
Take them as very large numbers.. sum will be a large number..
Hence this does not make a lot of sense!
I Guess NOT!