Expectation - June 19

[Amit Goyal]

June19__Expectation.png

[anon_econ]

Looks extremely difficult! :(
in the second part how can values of a1 and a2 maximize E(S(a1,a2))? i mean a1 and a2 r the variables in the random variable na? or was it supposed to be values of S1 and S2?

[Amit Goyal]

a1 and a2 are constants. And then choose a1, a2 that maximizes the expectation.

[anon_econ]

Ok. But i'm unable to do it.

[komal]

my answer is very weird, E value comes out to be 50 -  a1^2/ 200  +  a1/2  -   1/2 a1* a2^2 / 100^2  +a1a2/200,
and to maximise expected value a1 should be 62.5 and a2 = 50

[Amit Goyal]

Excellent work Komal. Now relate it to DSE 2011 Q40. Its exactly the same problem.

[Mr. Nobody]

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[komal]

Thanks :)

[komal]

we need to find E(s)which is equal to summation pisi,
there are three cases , so in first case, when S1>a1, summation pisi will be
integration 1/100  * x dx,from a1 to 100 ( for all the values of x>ai value of S(a1,a2) =S1=x)
in second case ,
summation pisi would be
 double integration ( a2 to 100) and from 0 to a1 1/100* 1/100*y dx.dy where y is the value of S2 and also S(a1,a2),
[ x is less than a1, and greater than a2]
 similar u can integrate for the third case ,
by adding all the three pisi , u will expected value of S(ai,a2).
I have written in a very complicated way , i hope this helps

[Mr. Nobody]

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