The histogram shows the distribution of stops for red traffic lights a commuter must pass through on her way to work. Use the histogram to find the mean, variance, standard deviation, and expected value of the probability distribution. 0 1 2 3 4 5 0.00 0.10 0.20 0.30 0.40 x P(x) 0.03 0.25 0.35 0.14 0.14 0.09 x y graph The mean is nothing. (Round to two decimal places as needed.)
Answer:
x 
P(x) 
x P(x) 
x^2 P(x) 
0 
0.03 
0 
0 
1 
0.25 
0.25 
0.25 
2 
0.35 
0.70 
1.40 
3 
0.14 
0.42 
1.26 
4 
0.14 
0.56 
2.24 
5 
0.09 
0.45 
2.25 
Totals 
2.38 
7.4 

=E(x) 
=E(x^2) 
Thus,
a)
Mean = E(x) = Expected value = 2.38
b)
Variance = E(x^2)  E(x)^2 = 7.4  (2.38)^2 = 1.7356
c)
Standard Deviation = sqrt [Variance] = sqrt(1.7356) = 1.3174
d)
E(x) = Expected value = mean = 2.38
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