<p>Consider tossing a fair coin twice in succession and we are interested in the random variable which represents the number of tails obtained.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: left; --cell-justify: flex-start">Outcome</th><th style="text-align: left; --cell-justify: flex-start">Probability</th><th style="text-align: left; --cell-justify: flex-start">Number of tails</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">\(HH\)</td><td style="text-align: left; --cell-justify: flex-start">\(\frac{1}{4}\)</td><td style="text-align: left; --cell-justify: flex-start">\(0\)</td></tr><tr><td style="text-align: left; --cell-justify: flex-start">\(HT\)</td><td style="text-align: left; --cell-justify: flex-start">\(\frac{1}{4}\)</td><td style="text-align: left; --cell-justify: flex-start">\(1\)</td></tr><tr><td style="text-align: left; --cell-justify: flex-start">\(TH\)</td><td style="text-align: left; --cell-justify: flex-start">\(\frac{1}{4}\)</td><td style="text-align: left; --cell-justify: flex-start">\(1\)</td></tr><tr><td style="text-align: left; --cell-justify: flex-start">\(TT\)</td><td style="text-align: left; --cell-justify: flex-start">\(\frac{1}{4}\)</td><td style="text-align: left; --cell-justify: flex-start">\(2\)</td></tr></tbody></table></div></div>
<p>Define \(X\) to be the number of tails obtained in two tosses of a fair coin.</p>
<p>In this case, \(X\) can only take on values from the finite set&nbsp;\(\{0,1,2\}\). To each of these values, we have:</p>
<p style="text-align: center">\[\mathrm{P}(X = 0) = \frac{1}{4}, \quad \mathrm{P}(X = 1) = \frac{1}{2}, \quad \mathrm{P}(X = 2) = \frac{1}{4}\]</p>
<p>So \(X\) is a random variable whose probability density function is given by</p>
<p style="text-align: center">\[\mathrm{f}_X(x) = \begin{cases} \frac{1}{4} & \text{if}\hspace{0.5em} x = 0 \\ \frac{1}{2} & \text{if}\hspace{0.5em} x = 1 \\ \frac{1}{4} & \text{if}\hspace{0.5em} x = 2 \end{cases}\]</p>

Consider tossing a fair coin twice in succession and we are interested in the random variable which represents the number of tails obtained.

Define \(X\) to be the number of tails obtained in two tosses of a fair coin.

In this case, \(X\) can only take on values from the finite set \(\{0,1,2\}\). To each of these values, we have:

\[\mathrm{P}(X = 0) = \frac{1}{4}, \quad \mathrm{P}(X = 1) = \frac{1}{2}, \quad \mathrm{P}(X = 2) = \frac{1}{4}\]

So \(X\) is a random variable whose probability density function is given by

\[\mathrm{f}_X(x) = \begin{cases} \frac{1}{4} & \text{if } x = 0 \\ \frac{1}{2} & \text{if } x = 1 \\ \frac{1}{4} & \text{if } x = 2 \end{cases}\]

Simple example of DRV involving number of heads

Simple example of DRV involving number of heads