Suppose that X is the number of bears spotted by tourists to Banff, Canada. The table below is the probability distribution for X. What is the expected value of X, that is, what is the mean of its distribution?

X 0 1 2 3 4

Probability 0.2 0.1 0.4 0.15 0.15

Expected value of X = 1.95

Step-by-step explanation:

Expected value of X, E (X) = ∑XP (X)

∑ = Summation

X = number of bears spotted

P (X) = probability of a certain number of bears spotted

E (X) = (0*P (X=0)) + (1*P (X=1)) + (2*P (X=2)) + (3*P (X=3)) + (4*P (X=4))

E (X) = (0*0.2) + (1*0.1) + (2*0.4) + (3*0.15) + (4*0.15)

E (X) = 0 + 0.1 + 0.8 + 0.45 + 0.60 = 1.95