Of course, the premise is that x and y are independent of each other.

The expected value of uniform distribution U(a, b) is (a+b)/2.

The expected value of exponential distribution E(λ) is 1/λ.

therefore

E(alnX+bY)

=4aE(lnX)+bE(Y)

= 4a *(LN2+ln 1)/2+b * 1/2

=2a*ln2 +b/2

=4ln2+2

So obviously,

a=2，b=4