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## Q. 1.2

Let the random variable X denote the maintenance cost for an antenna subjected to the wind, and presume that X=0 if the antenna is undamaged and \$5,000 (replacement cost) if it is damaged. How much information is needed to describe all probabilities of X ?

## Verified Solution

Because X has only two possible values in this simplified situation, one can describe all its probabilities with only one number $p= P(X = 5,000) = P(D)$, in which D denotes the event of antenna damage occurring. The 0nly other information that can be given about the random variable X is $P(X=0)= P(D^{C})=1-p$.