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  • Explain why the experiment of tossing a coin three times is said to have binomial distribution.

Explain why the experiment of tossing a coin three times is said to have binomial distribution.

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Let p= events of failure and q=events of success

It is known to us that,

A random variable X (=0,1, 2,…., n) is said to have Binomial parameters n and p, if its probability distribution is given by

\mathrm{P}(\mathrm{X}=\mathrm{r})=\mathrm{n}_{\mathrm{c}_{\mathrm{r}}} \mathrm{p}^{\mathrm{r}} \mathrm{q}^{\mathrm{n}-\mathrm{r}}$ \\Where, $q=1-p$ and $r=0,1,2, \ldots . . n$ \\In the experiment of a coin being tossed three times $\mathrm{n}=3$ and random variable $\mathrm{X}$ can take $\mathrm{q}=\frac{1}{2}$ values $r=0,1,2$ and 3 with $p=\frac{1}{2}$ and $q = \frac{1 }{2}

\begin{array}{|l|l|l|l|l|} \hline \mathrm{X} & 0 & 1 & 2 & 3 \\ \hline \mathrm{P}(\mathrm{X}) & 3_{\mathrm{c}_{0}} \mathrm{q}^{3} & 3_{\mathrm{c}_{1}} \mathrm{pq}^{2} & 3_{\mathrm{c}_{2}} \mathrm{p}^{2} \mathrm{q} & 3_{\mathrm{c}_{3}} \mathrm{p}^{3} \\ \hline \end{array}

Therefore, in the experiment of a coin being tossed three times,

we have random variable X which can take values 0,1,2 and 3 with parameters n=3 and p=\frac{1}{2}

Hence, tossing of a coin 3 times is a Binomial distribution.

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