Question

Suppose a coin is tossed three times.
(a) Using the "c" and "s" labels, list all possible outcomes in the sample space.
(b) For each result in the sample space, define the random variable X as the number of faces minus the number of stamps observed. Use the fact that all the results from part (a) have the same probability. Find the probability distribution of X.
(c) Use the probability distribution found in (b) to find the mean and standard deviation of X.

Answer 1

a) All possible outcomes in the sample space={(c,c,c),(c,c,s),(c,s,c),(s,c,c),(s,s,c),(s,c,s),(c,s,s),(s,s,s,)}

b) Given,they have similar probability,so,

X	P(X)
3
2-1=1
1-2=-1
0-3=-3

c)Mean of X=

Standard deviation of X=