Exercise: Normal

Assume \(x\) is a random variable from Normal Distribution with mean equal 6, and variance equal 25. Use this Information to answer the the questions.

  1. \[Pr(x<3)=\int_{-\infty}^{3}f(x)dx =\int_{-\infty}^{3} \frac{1}{\sqrt{2\pi 25}} e^{-\frac{(x-6)^2}{2\times 25}}dx\]

Answer: , Use 3 decimals to answer

  1. \[Pr(0<x<9)=\int_{0}^{9}f(x)dx =\int_{0}^{9} \frac{1}{\sqrt{2\pi 25}} e^{-\frac{(x-6)^2}{2\times 25}}dx\]

Answer: , Use 3 decimals to answer

  1. \[Pr(x>9)=\int_{9}^{\infty}f(x)dx =\int_{9}^{\infty} \frac{1}{\sqrt{2\pi 25}} e^{-\frac{(x-6)^2}{2\times 25}}dx\]

Answer: , Use 3 decimals to answer

  1. \[Pr(x< a)=\int_{-\infty}^{a}f(x)dx =\int_{-\infty}^{a} \frac{1}{\sqrt{2\pi 25}} e^{-\frac{(x-6)^2}{2\times 25}}dx=0.8\]

What is the value of a?

Answer: , Use 1 decimals to answer

Use Mean-Variance Criteria the made a decision, we assume the stock returns are the random variable from Normal Distribution.

Use the data from googledrive

  1. The average return of stock \(r_1\) = , and the SD of \(r_1=\) .

  2. The average return of stock \(r_2\) = , and the SD of \(r_2=\) .

  3. The average return of stock \(r_3\) = , and the SD of \(r_3=\) .

  1. With the mean-variance criteria Compare the stock \(r_1\) and \(r_2\),

Answer:

  1. With the mean-variance criteria Compare the stock \(r_2\) and \(r_3\),

Answer:

  1. With the mean-variance criteria Compare the stock \(r_1\) and \(r_3\),

Answer: