Math Answers

Consider a population consisting of 1,2,3,4 and 5. Supposed samples of size 3 are drawn from this population. describe the sampling distribution of the sample means.

• What is the mean and variance of the sampling distribution of the sample means?

1. Three coins are tossed and the random variable Y is the number of tail that appear.

Sample Space = ___

Y= _____

2 Let Z represent the number of girls (daughters) in a family of three children. Use B to represent boys and G 

to represent girls.

Sample Space = ______

Z=

 Doctors have become increasingly concerned about the sodium intake in the U.S. diet. Recommendations by the American Medical Association indicate that most individuals should not exceed 2400 mg of sodium per day. Liza ate 1 slice of pizza, 1 serving of ice cream, and 1 glass of soda for a total of 1030 mg of sodium. David ate 3 slices of pizza, no ice cream, and 2 glasses of soda for a total of 2420 mg of sodium. Melinda ate 2 slices of pizza, 1 serving of ice cream, and 2 glasses of soda for a total of 1910 mg of sodium. How much sodium is in one serving of each item?

Restriction: Use matrix inversion to answer to this question)

Peoples Limited has the following securities in issue:

• 1 million ordinary shares currently trading at N$1.30 each. The last dividend paid

amounted to 15.5 cents and the earnings and dividends of Peoples are expected

to grow at 4% per annum.

• 250 000 non-redeemable 7% preference shares with a nominal value of

N$1.10 each. These shares are currently trading at N$0.65 per share.

• 1 550 12% unsecured bonds with a nominal value of N$100 each

currently trading at N$85 each. These bonds are redeemable in 3 years’

time at the nominal value.

Required:

(a) Calculate the weighted average cost of capital for Peoples Limited using market

values. (10 marks)

(b) Is there another way to calculate the weighted average cost of capital?

Support your answer with a brief explanation. Define all terms used in

your answer.

Calculate the volume of the solid formed by revolving about the line y=1 the region bounded by the parabola

𝑥

2 = 4𝑦 and that line. Take the rectangular elements of area parallel to the axis of revolution.

Show that  p⟷q and (p∧ q) V (¬p ∧ ¬q) are logically equivalent.

Construct all random samples consisting three observations from the given data. Arrange the observations in ascending order without replacement and repetition.

86 89 92 95 98

Find the mean of the probability distribution of a random variable X, if P(X) = 20

X 1

for X =

1,2,3,4, and 5.

if u=(2,-3,4) & v=(-1,2,0)& w=(5,-1,2) find the angle b/n (u-2v) & (u+2w)

Perform what is being asked. Follow the steps indicated in the first column of the table to complete

the activity. In the second column, write your solution on the spaces provided. Situation: A population

of PWD learners in 5 schools in a certain municipality of Quezon Province are (x) 3, 7, 6, 13, and

17. Suppose that two schools were selected as samples, determine the mean and variance of the

sampling distribution of sample mean.

First Step:

Second Step:

a.

Third Step:

Fourth Step:

Fifth Step:

Sixth Step:

Seventh Step: