Conceptual Doubts from Q 21-60-DSE 2011

[Erika]

covering Q- 21 to 40 for now:

Q22. (i) is false as -1=/ 1=/ 0
           but for (ii) statement if we take x=5 (or any other real no.) 5 =/ -5...shouldnt ii also be false?

Q23. do we choose ans (c) b < 2 because when we shift sides of 4 in given eqn, we get:
        4y=x^2 (of the form: x^2=4py) ...which gives x^2 = (2)^2 * y. so b< 2 for origin. kindly confirm if this                        logic is right or wrong.

Q25. if x= 0 or not, but belongs to Q, it should be continuous ...why are we choosing option a?

Q29. I read the previously posted ans that the empty set and society are the two sets which would belong to club and tribe. but empty set is 'empty' and society is the universal set, so how are both in a club and tribe?

Q31, 32 How to go about this question?

Q 33, 34 Which formula of probability would be applicable here?

Q 36 how to find probability maximising allocations? 50 R and 50 G balls optimally distributed in 2 bags. maximise probability of picking Green is to be maximised.  

Q 37. Why do we choose option b? what makes a coefficient determinable and others non-determinable in OLS estimation?

Q 39. Are we saying it is upwardly biased because the difference between the proposed and estimated eqn is a2L (which is not present in estimated), so it pulls the regression upwards??

Q 40. Again, similar doubt. objective is to maximise score in three maximum chances. How do we cal his score for a retest?

Thanks a lot in case you're able to help!

Regards.

[maahi]

 39 ) der r 2 effects 1) l affects output positively 2) land k are positively related so upward bias
37 ) problem of multicollinearity read more on it
33) uniform dist
p(z<0.5) = p(x<0.5,y<0.5) + p(x>0.5,y<0.5) + p (X<0.5,y.0.5) = o.5*0.5*3

as pdf = a+b/2 = 1+0 / 2 = 0.5

34) p(z<0.5/ x= 0.75) = p (x=0.75,y<0.5 ) = o.5

[Erika]

oh yea...Multicollinearity..missed that
Thanks.
Ill practice more of those prob questions. thanks for solving maahi!

[Erika]

Alos, in Q 38. what is the logic to including ONE dummy variable?

[Sinistral]

22) why (i) is false?? infact if we do not take f(1) to be equal to 0 then f(1)=nf(1) because of the given property that f(xy)=f(x)+f(y).
and f(5) IS EQUAL TO f(-5) because ii says it is even function
so both are correct.

23) read parabola once again.

25) this has been discussed many times on this forum.
     in short I can say that u can always find an irrational number between 2 rational numbers so (for x <> 0) it will always be discontinuous. use continuity principle (LHL=RHL=value of the func) to see that it is continuous at x=0

31) 32) find  f_x(x) and f_y(y). total sum of all probabilities = 1

[Devika]

Hey maahi :)
Could you please explain why P(X<0.5) and P(Y<0.5) = 0.5 and why P(X=0.75)=1
I'm not very clear with Uniform Dist. I understand it, and can easily calculate the pdf, mean and variance. But not able to calculate the probabilities like the ones asked in this question. They baffle me!
Thank you!

[duck]

29) Its given in the question that the society and the empty set both are tribes.
And by definition :complement of a tribe is a club. So, society and empty sets are club as well.

36)Refer the following link:
http://discussion-forum.2150183.n2.nabble.com/DSE-2011-A-a-request-to-duck-Amit-Sir-Q40-plz-td7580464.html

40) Refer the following link
http://discussion-forum.2150183.n2.nabble.com/JNU-2010-td7580642.html#a7580644

[maahi]

ok ya i messed it

 0.5 is d median on d given interval so
p(x<0.5) = 0.5 = a+b/2 =median

pdf is 1/b-a

sorry

[Erika]

Thanks sinistral for helping. I understood others. But still dont know how to go about Q 31 and 32.
What does f_x(x) denote? Plus...the X and Y are given to have set intervals and their 'expected valued' are given. How would that be used?  

[Erika]

the ans key for 33 says ...0.75. we have gotten 0.5

[Erika]

wao. 29 was mind boggling for me..

and tnx a lot for the links duck!!

[Sinistral]

"X and Y are given to have set intervals"??
what does this mean?

X can take either 1 or -1. and Y can take any integer in between [1,6]
respective probabilities of p(x,y) are given in that table (for various combinations of (x,y)   )

f_x(x) is marginal pmf of p(x,y)  --- (as it is the discrete case i am using p(x,y) instead of f(x,y). in f_x(x), f_x imples f subscript x. btw, to be more correct i shud have written it as p_x(x)  )

so p_x(x) (in my earlier hint i wrote it as f_x(x) ) can be found by summing all the values of p(x,y) for a given x. ie separately for x=1 and x=-1
so p_x(x) = .1 + a +.3 + 0 + 0 +0 for x=1
similarly one can find p_x(x) for x=-1

and obviously  p_y(y) is calculated in the same way
Please see that it can be done in that table itself. An extra column is appended for p_x(x) and an extra row is appended for p_y(y)

now p_x(x) & p_y(y) will satisfy al the properties of pdf (or pmf in this case). so, always greater than zero and summation over entire domain = 1.

For eg: p_x(x=1) + p_x(x=-1) =1
and so on.
 

[Erika]

@sinistral with the detailed explaination, im almost there... p_x(x) relieved me ;)

so in the end we get a+b=0.3 from both p_x(x) and p_y(y). but to solve we would need two different equations ... clue on that plz?

[Erika]

oh also..this wont make a diff but just fir further ref, by mistake you have written x=1 when you have added for x=-1 and vice vera. :)

[Sinistral]

oh.. by mistake i calculated the value of p_x(x=1) at x=-1.

use the given E(X) and E(Y) (for p_x(x) and p_y(y) respectively) to get another equation in a & b

[Erika]

covering Q 41-60 here:

Q41, 42: I solved using Lagrange's equation but I get x1= 3 instead of 2 in Q41 and x2= 1 in              Q42.
        i feel i am missing on the function being defined as u(x1,x2)= min (function). What does MIN in a function like this imply??

Q 43. giffen and inferior is clear, (and i did read the posts on this before and it remains unresolved) but how would B be proven as a complementary good to A . With increase in price of A, she is buying ALL of A and NONE of B. isnt it that B is a supplement....one can replace coffee with tea completely. One cant replace all car with all petrol though (complementary)

Q 46.  why do we choose (c)? just a silly doubt...agent means consumer?? is this under 'exchange' topic?

Q 49. I know that in this que and also in Q 47, we can add the x1 & x2 and y1 & y2 to get sum = 10,10 which is the given endowment...but is this approach right?? Because I are not using the utility eqn anywhere. Maybe my method is flawed.

Q 52, 53, 54...plz give me a hint (or a link of this is discussed earlier..i could not find) on how to solve these..


Thanks a ton.

Regards.

[Erika]

cool. i got it ..

[maahi]

41 ) perfect complements case  where x and y should be equal
 so 2x1+ x2=x1+2x2  
 x1=x2
20x1 +30 x2 =100
20x1+30x1 = 100
x1= 100/50 = 2

42)
10x1 + 30 x2 = 100
40 x1 = 100
x1 = 2.5
 i think there is a typo in d ans . i can't figure it out as 2 how it can be 10 as then whole of income wud b spend in  consuming it  and 2 goods hv to be consumed tgether
 

46 )  yea..    c. as    6> 4 and according to d utility fn they hv to be equal  so anything which is in access its price is zero

[Erika]

fair enough for Q 41 and 42..we get the correct ans now! But even the ques we solve using lagrange's eqn looks the same (except the 'min' in the function) .If you could tell me how we decide if we have to use lagrange or consider this as a complementary good case.
Tnk u

[Erika]

also, regarding your doubt for Q 42.  I didnt get it well, but incase this helps:

2.5 is correct as.

(2.5)(10) + (2.5)(30) should = 100 for the case to be true

this implies ... 25+75 = 100..thus ans is correct if both have to be consumed simlutaneously