INVESTMENT ANALYSIS Paul Hunt is considering two business ventures. Th

Madeline Lott 2021-12-10 Answered
INVESTMENT ANALYSIS Paul Hunt is considering two business ventures. The anticipated returns (in thousands of dollars) of each venture are described by the following probability distributions:
\[\begin{array}{cc} Venture \ A & \\ \hline Earnings & Probability \\ \hline -20 & 3 \\ \hline 50 & 4 \\\hline 50 & 3 \\ \hline \end{array}\]
\[\begin{array}{cc} Venture \ B & \\ \hline Earnings & Probability \\ \hline -15 & 2 \\ \hline 30 & 5 \\\hline 40 & 3 \\ \hline \end{array}\]
a. Compute the mean and variance for each venture.
b. Which investment would provide Paul with the higher expected return (the greater mean)?
c. In which investment would the element of risk be less (that is, which probability distribution has the smaller variance)?

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Expert Answer

Bertha Jordan
Answered 2021-12-11 Author has 1632 answers
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 \(\displaystyle{\left({V}{\left({x}\right)}\right)}={E}{\left({x}^{{{2}}}\right)}–{\left({E}{\left({x}\right)}\right)}^{{{2}}}\)
\(\displaystyle{V}{\left({x}\right)}={885}-{\left({24}\right)}^{{{2}}}\)
\(\displaystyle{V}{\left({x}\right)}={885}-{576}\)
\(\displaystyle{V}{\left({x}\right)}={309}\)
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zurilomk4
Answered 2021-12-12 Author has 4818 answers
b)
Venture A investment would provide Paul with the higher expected return
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