Question

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 1

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