Probability and statistic question 1 Four coins fair are tos

1. Four coins (fair) are tossed and let X be the number of heads. (a) What is the sample Space? (b) What is the distribution table of X? (c) What are the mean and the variance of X? (d) Let A and B be the events that there are at least two heads and there is only one tail, respectively Find P(A|B).

Solution

a) Sample space = 0 head, 1 head, 2 heads, 3 heads and 4 heads

x = (0,1,2,3,4)

b)

Mean = E(x) = 2

Var = E(X^2)-mean^2

= 5-4 =1

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P(A/B) = P(atleast two heads and there is one head/there are three heads)

= 1 (as when there is 1 tail other 3 should be heads)

x	0	1	2	3	4	total
p	1/16	1/4	3/8	1/4	1/16	1
x*p	0	1/4	3/4	3/4	1/4	2
x^2*p	0	1/4	1 1/2	2 1/4	1	5