I had a question that I simiplified till the last step. However, I am not very comfortably withhave to calculate the expectations operator in a multiplicative/exponential setting.following: I know$$ E[a^{1/2}+b^{1/2}] $$ where $a=b=\frac{1}{2}\times10^{i}j$. We have that $a$$i$ is distributed uniformly ondistributed on say the $[0,1]$ interval and $b$$j$ is distrubtedalso uniformly distributed on the $[0,1].$ They$[0,1]$ interval. Both are both independent. HowI have canso far simplified this to: $$ E[2a^{1/2}]=2E[a^{^{1/2}}] $$ $E[a^{1/2}]$ is $E[(\frac{1}{2}\times10^{i}j)^{1/2})$. We know that $E[g(x,y)]=\int\int g(x,y)f(x,y)dxdy$. Substituting this for what we have, we obtain that $E[a^{1/2}]=\int\int(\frac{1}{2}10^{i}j)^{\frac{1}{2}}f(i,j)didj$. Given that $i$ and $j$ are independent, I simplifyobtain that the epxressionprevious $$ E[B^{a}b] $$expression simplifies to $\int\int\frac{1}{4}(10^{i}j)^{\frac{1}{2}}f(i)f(j)didj.$ Moreover, whereWe know that $B$ is a constant?$f(i)=f(j)=\frac{1}{2}.$ This then simplifies to $\frac{1}{16}\int\int10^{i}j\, didj$
I am stuck after this point and do not know the expectation operatorhow to proceed. Any help is linear, but the random variables are in exponential and multiplicative firm heremuch appreciated. Thanks a lot!