When we analyzed the interaction between algorithm M which is $(,\backslash$delta $)-$DP and the adversary A asking k adaptive questions we called the entire interaction

Among them W and we showed that for every query $\}$ q : U $->\{0,1$ it holds that

E

D$,$W$,$q$$W $($D$)[$q$($D e$$ ED$,$W$,$q$$W $($D$)[$q$($P $)]+\backslash$delta

Show that this holds for every query $-$ which is not necessarily binary, only non$-$negative.

That is$,$ show that if W outputs as a query output $]$ q : U $->[0,$ R then still holds that

E

D$,$W$,$q$$W $($D$)[$q$($D e$$ ED$,$W$,$q$$W $($D$)[$q$($P $)]+\backslash$delta

Hint: the expectancy of a non$-$negative random variable can be written as a sum$/$interval of probabilities