i tried to use the math code to type the question, but failed. hope you can understand what i typied there .thanx

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- November 29th 2008, 11:30 AM #1

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## g(E(X)) and E(g(X))

Who can help me get the part b).??

lex X be a descrete random variable and g:Rx →R a continous function, which is concave, ie for all x1,x2 in Rx and all k in range (0,1)

g(kx1 +(1-k)x2) >= k(g(x1)+(1-k)g(x2)

for all ki >=0 with

(\sum_{i=1}^{n}\{k_i=1})

and g(\sum_{i=1}^{n}\{k_i}{x_i}) \geq (\sum_{i=1}^{n}\{k_i}{g(x_i)})

Show that g(E(X))>= E(g(X))

- November 30th 2008, 05:27 AM #2

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- November 30th 2008, 06:02 AM #3
Hello,

Would this help : Jensen's inequality - Wikipedia, the free encyclopedia ?