Question 1132196: Let random variable x represent the number of heads when a fair coin is tossed three times.
(a) Construct a table describing the probability distribution.
(b) Determine the mean and standard deviation of x. Show all work. Just the answer, without supporting work, will receive no credit
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! There are 8 events in the sample space
:
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
:
Probability(P) (0 heads) = 1/8
:
P(1 head) = 3/8
:
P(2 heads) = 3/8
:
P(3 heads) = 1/8
:
(a) 0 heads p(0) = 1/8 = 0.125, 1 head p(1) = 3/8 = 0.375, 2 heads p(2) = 3/8 = 0.375, 3 heads p(3) = 1/8 = 0.125
:
x p(x)
---------
0 0.125
1 0.375
2 0.375
3 0.125
:
(b) mean(u) = (0 +1 +2 +3)/4 = 1.5
:
variance = ( (0-1.5)^2 +(1-1.5)^2 +(2-1.5)^2 +(3-1.5)^2 )/4 = 1.25
:
standard deviation = square root(variance) = square root(1.25) = 1.118
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