DSE 2010 Q 11,17 , 26 , 27 , 53, 54 , 57

[maahi]

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/option-a-2010.pdf

 plz help ...

[Sinistral]

17) the sequence is definitely not converging so it doesn't have a limit. but there are 2 limit points 1 and -1.
      u can read the difference between limit and limit points.

26)
f(Ө)= 1/pi ;-pi/2<Ө<pi/2
      = 0   ; elsewhere
P(X<x) = P(sinӨ<x) =P(Ө<   sin inverse x) = Integral [ x=-pi/2 to x= sin inverse x] 1/pi dӨ = <b>(sin inverse x)/pi + 1/2

27)
X~N(0, σ²)
(X-0)/ σ²  ~ N(0,1)
X^2/ σ² ~ chi square (1)   square of standard normally distributed rv is chi square distribution with r =1
so E[X^2/ σ²]=1    mean of chi square is = r (which is 1 in this case)
E[X^2] =  σ²

53)
we know that |x|-|y|<=|x+y|<=|x|+|y|
so |x|-|y|<=|x+y|
replacing y with -y
|x|-|y|<=|x-y|
so (i) is true

(ii) is false. Check with x=2 and y=-3

54)
It was explained somewhere in this forum quite formally.

[maahi]

thank you so much

[kogo]

plz anyone help me by explaining question no. 56, 58, 59, 60, 20
thank you in advance

[sakshi]

sinistral can u plz explain how n y u choose.. f(theta)=1/pie
 and range u took , from pie/2 to sin inverse x..??????????

[Sinistral]

because theta ~ U[-pi/2,pi/2]. Revise uniform distribution again.

I took range of theta from theta= -pi/2 to theta= sin inverse x.

why? because -pi/2 is the lower limit of U[-pi/2,pi/2].

[madhur1987]

in que 37 under buy 1 get 1 free scheme he can buy more amount of both x and y with same money income and increase his utility?? than why option a is not correct??