Question

Question 2 and Questions 3. All letter parts with detailed step by step answers please.

2 (20 pts + 5 pts) You are a financial analyst and use automotive company and its stock Y 5) and the company's monthly sales thes e o is the tablete Rate of return52311 um 5. 231415 Sales evaluation oodood 56759 10 11 12 1 6171. 710 d had pod a. Please calculate the geometrie man rate 2019 for the stock capa classes, build a percentage pal b. Using of return. (2 ) d o cive (2 pts) for the monthly rate c. You would like to categorize the valu t ate of return in 2019 into two ro 1 ) no larger than 3 (le, 53) and 2) larger than 3( 3). Whether the monthly rate of return > 3 is a categorical variable. Please construct a contingency table for whether the monthly rate of retum 18 > 3 and the monthly sales eraluation (use frequency for cell values) (2 pts). d. Based on your contingency table, calculate the probability of having a > 3 monthly rate of return (2 pts), the probability of having a "good" monthly sales evaluation (2 pts), the probability of having both a s 3 monthly rate of return AND a "bad" sales evaluation (2 pts), and the probability of having a s 3 monthly rate of return OR a "bad" sales evaluation (2 pts). e. What is the probability of having a > 3 monthly rate of return given that a bad monthly sales evaluation has occurred (2 pta)? Is the event, having a "bad" sales evaluation, Independent of having a > 3 monthly rate of return (2 pts)? "Bonus If an event A is independent with another event B. then A is also independent with its complement B'. Please prove this statement (5 pts). 3 (25 pts + 5 pts) For a new type of ffu, the number of infected individuals in a day follows a Poisson distribution The mean number of infected individuals in a day is 0.02. A pharmaceutical company developed a medication against this new flu. It claims that the medication has a probability of 0.8 to cure an infected person a. What is the probability of having NO infected individuals in 1000 people (2 pts)? What is the probability of having 1 infected individual in 1000 people (2 pts)? What is the probability of having 2 or more infected individuals in 1000 people (2 pts)? b. Let X = whether an infected person is cured by the medication. Please write down the prob- ability distribution of X (2 pts). What is the expected value (2 pts) and variance (2 pts) of X (please

Answer 1

2. (a.) The geometric mean of a set of n values is given as:

GM = 117=113

Putting the values in the formula we get

$GM=\sqrt[12]{5.2\times 3.1\times ...\times 3.0} = 3.72$

(b) The five classes can be determined as:

Class	Frequency
0-3	3
3_4	3
4_5	1
5_6	3
>6	2

Frequency Polygon 0-3 34 4_5 5_6 >6

(c.) The contingency table on the given data looks something like this:

	Sales Evaluation - "Good"	Sales Evaluation - "Bad'	Total
Return <= 3%	1	3	4
Return > 3%	5	3	8
Total	6	6	22

*Values in each box is determined by noting the frequency of values which satisfy both the criteria.

(d.) Remember that probability is given as:

Numberof FavorableOutcomes Probability = 2 Totalnumberof Outcomes

Probability of having a >3 monthly rate of return =

= 0.67

Probability of having a "good" monthly sales evaluation = $\frac{6}{12}=0.5$

Probability of having both a <= 3 monthly rate of return and a "bad" sales evaluation =$\frac{3}{12}=0.25$

Probability of having both a <= 3 monthly rate of return or a "bad" sales evaluation =

This probability can be determined using the additivity theorem, i.e. $P\left ( A \bigcup B \right )= P(A) + P(B)-P\left ( A\bigcap B \right )$

$P\left ( A \bigcup B \right )= P(Probability \, of \, having \, a <= 3 monthly rate ) + P(Probability \, of\, having \, a "bad" sales\, evaluation)-P\left ( Probability \, of\, having both\, a <= 3 monthly \, rate \, of \, return \, and \, a "bad" sales \, evaluation )$

Ths gives..

$\frac{4}{12}+\frac{6}{12}-\frac{3}{12}=\frac{7}{12}=0.5833$

(e) Probability of having a >3 rate of return given that a bad monthly sales evaluation occurs is given as:

$\frac{n(Bad \, Sales \, Evaluation \, and > Rate Of Return )}{n(Bad \, Sales\, Evaluation)}$

$\frac{3}{6}=0.5$