Math Answers

For a poisson random variable x having probably generating fuction G(t)= exp^?(t-1) . Show that the expected value E(x) and variance (x) are given by ?and ? Respectively

If a person's eye is x meters above the sea level, and she can see y meter in the horizon, then y=square root 3.75 square root x. What if the eye level is 5.29 meters above sea level, how far can she see in the horizon?

which of the following statements are true justify your answer

a) For any three set A,B,C in a universal set U,(A\B)×C=A×(B\C)

b) the operation of conjugation is closed on C

c) if f(x) and g(x) are polynomials for which f(0)= g(0) and f(t)= g(t) ,then f(x)=g(x)

d) the solution set of 2x= 1,y+5=x,x=y+3 is a singleton

Find the extreme values of

x^4+y^4-2(x-y)^2

Find the maximum value of

x^2y^3z^4

subject to the condition

x+y+z=5

Find the extreme values of

x^4+y^4-2(x-y)^2

Two duopolists produce and quantities of a homogenous product . The market demand of the product is given by Q= 240-2p where Q= Qa +Qb and the price of the product. The total functions of the duopolists are given by: C(Qa)= 60+4Qa and C(Qb)= 50+0.625Qb^2

a) Find the level of output that maximizes the profit of each firm and the corresponding profit

and price.

b) Find the level of output that maximizes their profit if the two firms corporate and the

corresponding profit and price.

Classify the following random variables as discrete or continuous.

a.the number of defective computers produced by a manufacturer.

b.the weight of newborns each year in a hospital.

c.the number of siblings in a family of a region.

d.the amount of paint utilized in a building project.

e.the number of dropout in a school district for a period of 10 years.

f.the speed of a car.

g.the number of female athletes.

h.the time needed to finish the test.

i.the amount of sugar in a cup of coffee.

j.the number of people who are playing LOTTO each day.

k.the number of accidents per year at an intersection.

l.the number of voters favoring a candidate.

m.the number of bushels of apples per hectare this year.

n.the number of patient arrivals per hour at a medical clinic.

o.the average amount of electricity consumed per household per month.

p.the number of deaths per year attributed to lung cancer.

Formulate the null hypotheses and alternative hypotheses for the following:

1.) Children who eat oily fish for certain period of time have a higher IQ.

2.) A researcher believes the coffee consumption increase the heart beat rate.

3.) A university is claiming that the passing rate of each Bachelor of Science and 

Nursing in the licensure examination is higher than 69% national passing rate.

4.) The average salary of the faculty in the college is 8,900 pesos. In another college, the average salary of 30 chosen employees is 9,500 pesos with standard deviation of 1750.

5.) A CEO of a company is claiming that 80% of the costumers are satisfied with the company service.

6.) A drug has developed a drug that can prevent colds. The company claims that the drug has the same effect in the men and women.

A group of researchers conduct a research about fertility among Malaysian citizens. Data obtained from the research are as followed:

A = number of siblings that a married couple has

B = number of children that a married couple has

Table 1

A

3

4

4

6

7

9

B

2

5

5

6

4

4

Determine the statistics analysis method if you want to find the relationship between A and B.

Is there exists a relationship between A and B?

Plot a scatter diagram for Table 1. Draw the regression line on the diagram.