Math Answers

This refers to the characteristics of math language that it uses symbols to express more. A. Precise C. Complex

B. Concise D. Powerful

___2. Which of the following expressions is NOT equivalent to the group? A. 1+ 1+ 1+ 1+ 1 + 1 C. 39 + 45 – 78

B. { | n = 3} D. 23

___3. Translate the expression “twice of k less than four”

A. 2k – 4 C. 4 – 2k

B. 2k < 4 D. k2 - 4

___4. Which of the following is the mathematical sentence for a2+ b2= c2? A. the Pythagorean Theorem

B. The sum of squares of a and b is equal to the square of c

C. The squares of a, b, and c

D. Twice the sum of a and b is equal to twice of c

An educator claims that the average IQ of American college student is at most 110, and

that in a study made to test this claim 150 American college students selected at random had

an average IQ of 111.2 with a standard deviation of 7.2. Use a level of significance of 0.01

to test the claim of the educator.

Let 𝑋1, … , 𝑋𝑛 be iid Gamma(1, 1/𝛼) RVs

(a) Show that the estimator T(𝑋1, … , 𝑋𝑛) = (n-1)/n𝑋̅ is the UMVUE for 𝛼 with 

variance 𝛼²/(𝑛 − 2)

(b)Show that the minimum variance from CR inequality is 𝛼²/𝑛

The table below shows the frequency distribution for the variable level of satisfaction with nursing care by 475 women in the maternal health ward at hospital X.

Level of satisfaction. Frequency

Very satisfied. 121

Satisfied. 161

Neutral. 90

Dissatisfied. 51

Very dissatisfied. 52

(I) what measure of location can you established from this data?

(Ii) find the measure of location in (I)

(Iii) What measure of location is appropriate to describe the data set?

(Iv) Draw a pie chart and bar graph for the data and briefly interpret

 Let 𝑋1, … , 𝑋𝑛 be a random sample from the Bernoulli distribution, 

say P[X=1] = θ=1-P[X=0]. (a) Find the CRLB for the variance of unbiased estimators of 

θ(1-θ). (b) Find the UMVUE of θ(1-θ) if such exists.

A herd of 1,500 steer was fed a special high‐protein grain for a month. A random sample of 29 were weighed and had gained an average of 6.7 pounds. If the standard deviation of weight gain for the entire herd is 7.1, test the hypothesis that the average weight gain per steer for the month was more than 5 pounds.

The probability distribution shown represents the number of trips of five nights or more that American adults take per year. (That is, 6% do not take any trips lasting five nights or more, 70% take one trip lasting five nights or more per year, etc.) Find the mean.

Find the height of a trapezoid with area of 99m2 and the bottom base is twice the top base, which measures 6m.

Find the Wronskian of the following functions and determine whether it is linearly dependent or linearly independent on (-∞,∞).

{x2, x+1, x-3} ans, W=8, linearly independent

{3e2x, e2x} ans, W=0, linearly dependent

{x2, x3, x4} ans, W=2x^6, linearly independent

Check that {1,(x+1),(x+1)^2} is a basis of the vector space of polynomial over R of degree at most 2. Find the coordinate of 3+x+2x^2 with respect to the basis.