Question

Let T be a random variable giving the number of heads in

three tosses of a coin. List the elements of the sample

space S for the three tosses of the coin and assign a value

to each sample point.

Answer 1

Sample space $S$ is,

$S=\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\}$

$T$ is a random variable denoting the number of heads therefore, it may take on the values 0,1,2,3. This can be written as, $t=0,1,2,3$.

In assigning values to each sample point, the value $t$ is the number of heads in the respective sample point. The values have been assigned below.

Sample point. value (t)

HHH 3

HHT 2

HTH 2

HTT 1

THH    2

THT     1

TTH 1

TTT         0