Question

) Below is a table giving the probabilities for different outcomes. Outcome 0.5 1.5 2 5.5 Probability 0.35 0.15 0.15 0.35 Find the expected value.

Answer 1

Solution:
Discrete probability distribution table can be written as follows:

X	P(X)
0.5	0.35
1.5	0.15
2	0.15
5.5	0.35

Total probability of this discrete probability distribution is
P(X=0.5) + P(X=1.5) + P(X=2) + P(X=5.5) = 0.35 + 0.15 + 0.15 + 0.35 = 1
Expected value can be calculated as
Expected value = (Xi*P(Xi)) = (0.5*0.35) + (1.5*0.15) + (2*0.15) + (5.5*0.35) = 0.175 + 0.225 + 0.3 + 1.925 = 2.625

X	P(X)	Xi*P(Xi)
0.5	0.35	0.175
1.5	0.15	0.225
2	0.15	0.3
5.5	0.35	1.925

So Expected Value = 2.625