A person plays a game of tossing a coin thrice. For each head, he is given Rs 2 by the organiser of the game and for each tail, he has to give Rs 1.50 to the organiser. Let X denotes the amount gained or lost by the person. Show that X is a random variable and exhibit it as a function on the sample space of the experiment.

Explanation

is random variable`Y`

domain of y = sample space``

Co-domain= real no.``

S= { (HHH),(HHT),(THH),(HTH),(TTH),(THT),(HTT),(TTT)}``

`X=2xx`(no of heads)-1.5(no.of tails)

X(HHH)`=2xx3-1.5xx(0)=Rs6`

X(HHT)`=X(HTH)=X(THH)=2xx2-1.5(1)`

`=4-1.5`

...