The following table contains the probability distribution for the number of traffic accidents (X) daily in a small town:
No of accidents (X)
0
1
2
3
4
5
P(X)
0.15
0.2
B
0.15
0.15
0.15
Determine:
E[X]
E[X] = Σ(X * P(X)) = 0*0.15 + 1*0.2 + 2*B + 3*0.15 + 4*0.15 + 5*0.15
Since the probabilities must sum up to 1, we can find the value of B by summing up all probabilities and setting it equal to 1:
0.15 + 0.2 + B + 0.15 + 0.15 + 0.15 = 1
0.8 + B = 1
B = 0.2
Now we can substitute the value of B back into the equation for E[X]:
E[X] = 0*0.15 + 1*0.2 + 2*0.2 + 3*0.15 + 4*0.15 + 5*0.15
E[X] = 0 + 0.2 + 0.4 + 0.45 + 0.6 + 0.75
E[X] = 2
Therefore, the expected number of traffic accidents daily in the small town is 2.