91影视

Three coins are tossed.

The likelihood that a comparable continuous random variable has a value less than or equal to the function's argument is the value of the function.

Let S be the sample space.

$S=\{HHH,HHT,HTH,HTT,THH,THT,THH,TT\}$

Find the random variable.

Find the value of .$x_1$

$\begin{array}{c}H=0\\ T=3\\ x_1=鈭�3\\ p_1=1/8\end{array}$

Find the value of role="math" $x_2$.

$\begin{array}{c}H=1\\ T=2\\ x_2=鈭�1\\ p_2=3/8\end{array}$

Find the value of $x_3$.

$\begin{array}{c}H=2\\ T=1\\ x_3=1\\ p_1=3/8\end{array}$

Find the value of $x_4$

$\begin{array}{c}H=3\\ T=0\\ x_4=3\\ p_4=1/8\end{array}$

The mean is given below.

$\begin{array}{c}渭=鈭�x_i{p}_i\\ 渭=鈭�3脳\frac{1}{8}鈭�\frac{3}{8}+\frac{3}{8}+3脳\frac{1}{8}\\ 渭=0\end{array}$

The variance is given below.

$\begin{array}{c}\mathrm{var}\left(x\right)=鈭�{\left(x_i鈭�渭\right)}^2\\ p_i=鈭�x_i^2{p}_i\\ =脳\frac{1}{8}脳\frac{3}{8}+脳\frac{3}{8}+脳\frac{1}{8}\\ \mathrm{var}\left(x\right)=3\end{array}$

The standard deviation is given below.

$\begin{array}{c}蟽=\sqrt{\mathrm{var}\left(x\right)}\\ 蟽=\sqrt{3}\end{array}$

Cumulative function is given below.

$\begin{array}{c}{x}_1=鈭�3\\ F(鈭�3)=1/8\\ x_2=鈭�1\\ F(鈭�1)=1/2\end{array}$

Solve further.

$\begin{array}{c}{x}_3=1\\ F\left(1\right)=7/8\\ x_4=3\\ F\left(3\right)=1\end{array}$

Thegraph is shown below.