Question

STATISTICS/PROBABILITY: Let X= the # of heads when 4 coins are tossed.

a.) Find the expected number of heads

b.) Find the variance and standard deviation

so far I have

x	0	1	2	3	4
P(x)	1/16	4/16	6/16	4/16	1/16

Answer 1

Solution:

The formula for expected number and variance and standard deviation are given as below:

Expected number = mean = ∑XP(X)

Variance = ∑ P(X)*(X - mean)^2

Standard deviation = Sqrt(Variance)

The calculation table is given as below:

X	P(X)	XP(X)	P(X)*(X - mean)^2
0	0.0625	0	0.25
1	0.25	0.25	0.25
2	0.375	0.75	0
3	0.25	0.75	0.25
4	0.0625	0.25	0.25
Total	1	2	1

Expected number = mean = ∑XP(X) = 2

Expected number = 2

Variance = ∑ P(X)*(X - mean)^2 = 1

Variance = 1

Standard deviation = Sqrt(Variance) = sqrt(1) = 1

Standard deviation = 1