If three fair coins are tossed, then variance of number of heads obtained, is

Question

Aicharya · Accepted Answer

Let r.v X denotes the no. of heads obtained $\therefore \quad$ Probability distribution of X is given as

$\begin{aligned} \mathrm{E}(x) & =0 \times \frac{1}{8}+1 \times \frac{3}{8}+2 \times \frac{3}{8}+3 \times \frac{1}{8}=\frac{3}{2} \\ \mathrm{E}\left(x^2\right) & =0 \times \frac{1}{8}+1 \times \frac{3}{8}+4 \times \frac{3}{8}+9 \times \frac{1}{8}=3 \\ \therefore \quad \mathrm{~V}(x) & =\mathrm{E}\left(x^2\right)-[\mathrm{E}(x)]^2 \\ & =3-\frac{9}{4} \\ & =\frac{3}{4} \\ & =0.75\end{aligned}$

If three fair coins are tossed, then variance of number of heads obtained, is

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