GATE CSE 2006 | Question: 18

Question

We are given a set $X = \{X_1,\ldots,X_n\}$ where $X_i=2^i$.  A sample  $S\subseteq X$ is drawn by  selecting each $X_i$  independently with probability $P_i = \frac{1}{2}$ . The expected value of the smallest number in sample $S$ is:

• A. $\left(\frac{1}{n}\right)$
• B. $2$
• C. $\sqrt n$
• D. $n$

Comments

Option D is correct 
some of best answer is present in other comments but i’ll give you visula for this question

suppose there where 8 elements in X ={2,4,8,16,32,64,128,256}       n=8
Sample space S has probability ½ this means 1 in any 2 element is chosen size of sample space will be n/2 and then middle elements will be chosen 

{2,4,8,16,32,64,128,256}     
min(8,16,32,64)=8
n=8 hence expected value is n

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THANKS VAIBHAV.

MUCH NEEDED

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 A sample  S⊆ X is drawn by  selecting each Xi  independently with probability P i=½ means...

 

Answer 1

Most probably 2 option b not sure.

Comments

D is correct !