DSE 2012

[neha:)]

Q. 14. Integrate from 0 to 1 : (x^n)sin x dx
a. doesn't exist
b. necessarily greater than 1
c. greater than 1/(n+1)
d. less than 1/(n+1)


Q.5. Sania and Saina are bargaining over how to split 10 Rs. Both claimants simulatneously name shares they would like they would like to have s1 and s2, where s1, s2 belongs to [0,10]. If s1+s2 is less than equal to 10 then the claimants receive the shares they named; otherwise both receive zero. Find all pure strategy Nash Equilibrium of this game.
a. s1 =5, s2 =5
b. {(s1, s2) | s1 + s2 =10}
c. {(s1, s2) | s1 + s2 is less than equal to 10}
d. no pure strategy nash eqb.

[kangkan]

dnt knw 14....15..lets take (5,5) this clearly is a nash equilibrim...so we have one..now lets check other options..  (6,3)-this is not a nash equlibrium cuz the agent 2 has an incentive to change behaviour when the choice of agent 1 is revealed...so s1+s2<10 cant be nash equli...now lets check (7,3)..this is nash equi..no agent has an incentive to change behaviour...for that matter all allocations s1+s2=10 will be nash equi :)

[mrittik]

value of sinx<1, integration of this we get it is less than 1/(n+1)

[Bankelal]

Try out with x^n sinx< x^n for x<half(pie).

Thus it will always be less than 1/(n+1).

On Mon, May 19, 2014 at 9:49 PM, neha:) [via Discussion forum] <[hidden email]> wrote:

Q. 14. Integrate from 0 to 1 : (x^n)sin x dx
a. doesn't exist
b. necessarily greater than 1
c. greater than 1/(n+1)
d. less than 1/(n+1)


Q.5. Sania and Saina are bargaining over how to split 10 Rs. Both claimants simulatneously name shares they would like they would like to have s1 and s2, where s1, s2 belongs to [0,10]. If s1+s2 is less than equal to 10 then the claimants receive the shares they named; otherwise both receive zero. Find all pure strategy Nash Equilibrium of this game.
a. s1 =5, s2 =5
b. {(s1, s2) | s1 + s2 =10}
c. {(s1, s2) | s1 + s2 is less than equal to 10}
d. no pure strategy nash eqb.

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[neha:)]

Got it! Thanks :)

[SoniaKapoor]

i didnt get the sine one now also...pls explainn

[kangkan]

integrate it by parts ..let X^ndx=dv and sinx=u..


we get I= X^n+1/n+1 - int (from 0 to 1) cosx *X^n+1 /(n+1)dx...now X^(n+1)cosX is always positive in the int 0 to 1.   hence 1/n+1 - something...hence it will be always less than 1/n+1

[bhavya jain]

someone plz explain this question
9) Suppose X is a RV, which follows uniform [-1,1]. Find the covariance b/w X & X^2.
a)1
b)1/4
c)1/8
d)0

[Dreyfus]

The PDF of uniform distribution is given by f(x)=1/b-a where b=1 and a=-1, f(x)=1/2
The rth moment about origin ie E(X^r) for cont rv is given by integration of (x^r)*f(x){from -1 to 1 in this case}
E(X)=integrate x/2 from -1 to 1=0
E(X²)=integrate x²/2 from-1 to 1=1/3
E(X³)=integrate x³/2 from -1to1=0
Cov(X,X²)=E(X³)-E(X)*E(X²)=0

[The Villain]

@kangkan why is (6,3) not a nash eqm bt (7,3) is??

[kangkan]

lets assume i called 3..when i know that the other player has called 6, i will have an incentive to change my behaviour and call 4....since,players cant have incentive to change behaviour when choices are revealed for nash qui, (6,3) cant be a nash equilibrium

[The Villain]

Thnxx kangkan :-)

[kangkan]