Question 181542
P(1)=10/10=1/2
P(2)=5/20=1/4
P(5)=3/20
P(10=1/20
P(100)=1/20
:
X(1)-payout if X is 1 
X(2)-payout if X is 2
X(5)-payout if X is 5
X(10)payout if X is 10
X(100)payout if X is 100
:
the probability of each event * the payout of each event is added all up to give the expected value of X

:
{{{E(X)=((1/2)(1))+((1/4)(2))+((3/20)(5))+((1/20)(10))+((1/20)(100))}}}
:
{{{E(X)=(1/2)+(1/2)+(3/4)+(1/2)+5}}}
:
{{{E(X)=5+9/4= highlight(7.25)}}}