Question

Construct the probability distribution for the random variables describe each following situations. Draw the corresponding histogram for each probability distribution. Label it properly

1. Let T be a random variable giving the number of tails 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.

Valueof the Random Variable T

(Number of Tails)

Probability P(T)

Answer 1

Sample space S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

There are total 8 sample space

The value of T can be 0,1,2,3

$P(T=0)=\dfrac{1}{8}$

$P(T=1)=\dfrac{3}{8}$

$P(T=2)=\dfrac{3}{8}$

$P(T=3)=\dfrac{1}{8}$

Probability Distribution is-

and Histogram is-