Given

Venture A

\[\begin{array}{|c|c|}\hline Earnings & Probability \\ \hline -20 & 0.3 \\ \hline 40 & 0.4 \\ \hline 50 & 0.3 \\ \hline \end{array}\]

Venture B

\[\begin{array}{|c|c|}\hline Earnings & Probability \\ \hline -15 & 0.2 \\ \hline 30 & 05 \\ \hline 40 & 0.3 \\ \hline \end{array}\]

For Venture A

Mean \(\displaystyle{\left({E}{\left({x}\right)}\right)}=\sum{X}.{P}{\left({x}\right)}\)

\(\displaystyle{E}{\left({x}\right)}={\left(-{20}\times{0.3}\right)}+{\left({40}\times{0.4}\right)}+{\left({50}\times{0.3}\right)}\)

\(\displaystyle{E}{\left({x}\right)}=-{6}+{16}+{15}\)

\(\displaystyle{E}{\left({x}\right)}={25}\)

\(\displaystyleΕ{\left({x}^{{{2}}}\right)}=\sum{x}^{{{2}}}.{P}{\left({x}\right)}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={\left(-{20}^{{{2}}}\times{0.3}\right)}+{\left({40}^{{{2}}}\times{0.4}\right)}+{\left({50}^{{{2}}}\times{0.3}\right)}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={120}+{640}+{750}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={1510}\)

Variance \(\displaystyle{\left({V}{\left({x}\right)}\right)}={E}{\left({x}^{{{2}}}\right)}–{\left({E}{\left({x}\right)}\right)}^{{{2}}}\)

\(\displaystyle{V}{\left({x}\right)}={1510}-{\left({25}\right)}^{{{2}}}\)

V(x)=1510-625

V(x)=885

For Venture B

Mean \(\displaystyle{\left({E}{\left({x}\right)}\right)}=\sum{X}.{P}{\left({x}\right)}\)

\(\displaystyle{E}{\left({x}\right)}={\left(-{15}\times{0.2}\right)}+{\left({30}\times{0.5}\right)}+{\left({40}\times{0.3}\right)}\)

\(\displaystyle{E}{\left({x}\right)}=-{3}+{15}+{12}\)

\(\displaystyle{E}{\left({x}\right)}={24}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}=\sum{x}^{{{2}}}.{P}{\left({x}\right)}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={\left(-{15}^{{{2}}}\times{0.3}\right)}+{\left({30}^{{{2}}}\times{0.4}\right)}+{\left({40}^{{{2}}}\times{0.3}\right)}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={45}+{360}+{480}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={885}\)

Variance \(\displaystyle{\left({V}{\left({x}\right)}\right)}={E}{\left({x}^{{{2}}}\right)}–{\left({E}{\left({x}\right)}\right)}^{{{2}}}\)

\(\displaystyle{V}{\left({x}\right)}={885}-{\left({24}\right)}^{{{2}}}\)

\(\displaystyle{V}{\left({x}\right)}={885}-{576}\)

\(\displaystyle{V}{\left({x}\right)}={309}\)

Venture A

\[\begin{array}{|c|c|}\hline Earnings & Probability \\ \hline -20 & 0.3 \\ \hline 40 & 0.4 \\ \hline 50 & 0.3 \\ \hline \end{array}\]

Venture B

\[\begin{array}{|c|c|}\hline Earnings & Probability \\ \hline -15 & 0.2 \\ \hline 30 & 05 \\ \hline 40 & 0.3 \\ \hline \end{array}\]

For Venture A

Mean \(\displaystyle{\left({E}{\left({x}\right)}\right)}=\sum{X}.{P}{\left({x}\right)}\)

\(\displaystyle{E}{\left({x}\right)}={\left(-{20}\times{0.3}\right)}+{\left({40}\times{0.4}\right)}+{\left({50}\times{0.3}\right)}\)

\(\displaystyle{E}{\left({x}\right)}=-{6}+{16}+{15}\)

\(\displaystyle{E}{\left({x}\right)}={25}\)

\(\displaystyleΕ{\left({x}^{{{2}}}\right)}=\sum{x}^{{{2}}}.{P}{\left({x}\right)}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={\left(-{20}^{{{2}}}\times{0.3}\right)}+{\left({40}^{{{2}}}\times{0.4}\right)}+{\left({50}^{{{2}}}\times{0.3}\right)}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={120}+{640}+{750}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={1510}\)

Variance \(\displaystyle{\left({V}{\left({x}\right)}\right)}={E}{\left({x}^{{{2}}}\right)}–{\left({E}{\left({x}\right)}\right)}^{{{2}}}\)

\(\displaystyle{V}{\left({x}\right)}={1510}-{\left({25}\right)}^{{{2}}}\)

V(x)=1510-625

V(x)=885

For Venture B

Mean \(\displaystyle{\left({E}{\left({x}\right)}\right)}=\sum{X}.{P}{\left({x}\right)}\)

\(\displaystyle{E}{\left({x}\right)}={\left(-{15}\times{0.2}\right)}+{\left({30}\times{0.5}\right)}+{\left({40}\times{0.3}\right)}\)

\(\displaystyle{E}{\left({x}\right)}=-{3}+{15}+{12}\)

\(\displaystyle{E}{\left({x}\right)}={24}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}=\sum{x}^{{{2}}}.{P}{\left({x}\right)}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={\left(-{15}^{{{2}}}\times{0.3}\right)}+{\left({30}^{{{2}}}\times{0.4}\right)}+{\left({40}^{{{2}}}\times{0.3}\right)}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={45}+{360}+{480}\)

\(\displaystyle{E}{\left({x}^{{{2}}}\right)}={885}\)

Variance \(\displaystyle{\left({V}{\left({x}\right)}\right)}={E}{\left({x}^{{{2}}}\right)}–{\left({E}{\left({x}\right)}\right)}^{{{2}}}\)

\(\displaystyle{V}{\left({x}\right)}={885}-{\left({24}\right)}^{{{2}}}\)

\(\displaystyle{V}{\left({x}\right)}={885}-{576}\)

\(\displaystyle{V}{\left({x}\right)}={309}\)