Question

A coin was flipped four times. Let T be the number of tails that come out.

A. Construct the probability distribution of the random variable

B.Construct the probability histogram

Answer 1

A.

There are $2^4=16$ possible outcomes

$$S=\{HHHH, HHHT, HHTH, HTHH, THHH,$$

$$HHTT, HTHT, HTTH, THTH, THHT, TTHH,$$

$$HTTT, THTT, TTHT, TTTH, TTTT\}$$

The possible values of the random variable $T$ are $0, 1, 2, 3, 4.$

We will assume that the probability of getting heads and tails is the same:

$$p = q =1/2$$

Construct the probability distribution of the random variable

$$\def\arraystretch{1.5} \begin{array}{c:c} t & 0 & 1 & 2 & 3 & 4 \\ \hline p(t) & 1/16 & 1/4 & 3/8 & 1/4 & 1/16 \end{array}$$

or

$$\def\arraystretch{1.5} \begin{array}{c:c} t & 0 & 1 & 2 & 3 & 4 \\ \hline p(t) & 0.0625 & 0.25 & 0.375 & 0.25 & 0.0625 \end{array}$$

B.Construct the probability histogram