Question

3. Let W be a random variable giving the number of heads minus 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 to each sample point assign a value w of W.

Answer 1

Let, \(W\) be a random variable giving the number of heads minus the number of tails in three tosses of a coin

i.e., \(W=(\) Number heads \(-\) Number of tails) in throwing of a coin thrice

Here, the sample space

\(S=\{H H H, H H T, H T H, H T T, T T T, T T H, T H T, T H H\}\)

Here \(W=w\) with \(w=3,1,-1,-3\)

\(W=\left\{\begin{aligned} \text { 3, With HHH } \\ \text { 1, With HHT, HTH, THH } \\-1 \text { , With TTH, THT, HTT } \\ \text { -3, With TTT } \end{aligned}\right\}\)