Step 1

Given information-

\(\displaystyle\mu_{{1}}={0.0001},\sigma_{{1}}={0.01},\mu_{{2}}=-{.0002},\sigma_{{2}}={0.015},{\quad\text{and}\quad}ρ={.45}\).

Using \(\displaystyle{z}_{{s}}={\left\lbrace{0.814},{0.259}\right\rbrace}\)

So, X = 0.814, Y = 0.259

Step 2

So,

\(\displaystyle{z}_{{1}}=\frac{{{X}-\mu_{{1}}}}{\sigma_{{1}}}\)

\(\displaystyle{z}_{{1}}=\frac{{{0.814}-{0.0001}}}{{0.01}}={81.39}\)

\(\displaystyle{z}_{{2}}=\frac{{\frac{{{Y}-\mu_{{2}}}}{\sigma_{{2}}}-{p}{z}_{{1}}}}{{\sqrt{{{1}-{p}^{{2}}}}}}\)

\(\displaystyle{z}_{{2}}={\left(\frac{{{0.259}-{\left(-{0.0002}\right)}}}{{0.015}}-{0.45}\times{81.39}\right)}={21.6628}\)

So, the value of, \(\displaystyle{z}_{{1}}={81.39}{\quad\text{and}\quad}{z}_{{2}}=-{21.6628}\).

Given information-

\(\displaystyle\mu_{{1}}={0.0001},\sigma_{{1}}={0.01},\mu_{{2}}=-{.0002},\sigma_{{2}}={0.015},{\quad\text{and}\quad}ρ={.45}\).

Using \(\displaystyle{z}_{{s}}={\left\lbrace{0.814},{0.259}\right\rbrace}\)

So, X = 0.814, Y = 0.259

Step 2

So,

\(\displaystyle{z}_{{1}}=\frac{{{X}-\mu_{{1}}}}{\sigma_{{1}}}\)

\(\displaystyle{z}_{{1}}=\frac{{{0.814}-{0.0001}}}{{0.01}}={81.39}\)

\(\displaystyle{z}_{{2}}=\frac{{\frac{{{Y}-\mu_{{2}}}}{\sigma_{{2}}}-{p}{z}_{{1}}}}{{\sqrt{{{1}-{p}^{{2}}}}}}\)

\(\displaystyle{z}_{{2}}={\left(\frac{{{0.259}-{\left(-{0.0002}\right)}}}{{0.015}}-{0.45}\times{81.39}\right)}={21.6628}\)

So, the value of, \(\displaystyle{z}_{{1}}={81.39}{\quad\text{and}\quad}{z}_{{2}}=-{21.6628}\).