MATH TERMS FOR BOARDS

A ________ is a procedure that answers the question "Did these data come from a particular type of distribution?"

hypothesis test

The unit of ▽ x H is ______.

ampere/meter²

In signal flow graph, what refers to the node that has both income and outgoing branches?

Chain node

If the poles or zeros are repeated, then the function is said to be having __________ poles or ________ zeros.

multiple, multiple

The differential equation in the form of y' = P(x)y² + Q(x)y + R(x) is called a/an _____.

Ricatti equation

The equation y" + p(x)y' + q(x)y = 0 is a _____ equation.

second-order linear homogeneous

Find the general solution of the differential equation y" - k²y = 0.

y = A cosh (kt) + B sinh (kt)

______ are determinants of submatrices associated with particular entries in the original square matrix.

Cofactors

Determine the initial value of the time-domain response of the following equation using the initial-value theorem. Y(s) = 2s/(s + 1)²(s + 2).

2

What gives the cumulative probability that a numerical event will be less than or equal to event X?

Probability distribution factor

What is the ROC of z-transform of finite duration anti-causal sequence?

Entire z-plane, except at z = ∞

In signal flow path, what refers to the path from output node or a node near output node to a node near input node without repeating any of the nodes in between them?

Feedback path

Which of the ff. are true statements?

I. If the sample has variance zero, the variance of the population is zero.

II. If the population has variance zero, the variance of the same is also zero.

III. If the sample has variance zero, the sample mean and the sample median are equal.

II and III

What is the cardinality of a power set of a set S of cardinality n?

2ⁿ

The sum of the squares of two positive number is 200. Their minimum product is _____.

no minimum product exist

"If y = f(x) is continuous on the interval [a, b], and is differentiable everywhere on the interval (a, b) and if f(a) = f(b) = 0, then there is at least one number c between a and b such that f'(c) = 0." This is known as _____.

Rolle`s theorem

A _______ X on a sample space S is a function from S into the set R of real numbers such that the preimage of every interval of R is an event of S.

random variable

An _______maximum or minimum occurs either at an artificial point or an end point.

absolute

The general solution of the differential equation dy/dx = (1 - 2x)/y is a family of ______.

ellipses

According to Newton's law of cooling, the temperature of an object decreases at a rate proportional to the difference between its temperature and that of the surrounding air. Suppose a corpse at a temperature of 32°C arrives at a mortuary where the temperature is kept at 10°C. Then the differential equation satisfied by the temperature T of the corpse t hr later is _____.

dT/dt = - k(T - 10)

A class of graphs that is closed under isomorphism is called a ______.

graph property

_____ is the set of all possible outcomes of a probability experiment.

Sample space

What is the t-tests (based on Student's distribution) useful for?

Determining if the differences between samples mean is significant.

A convenient way of describing a process (stochastic) and computing the probability of any event is by a _______.

tree diagram

What refers to a function with two arguments, each of which can be assigned any nonnegative integer, that is, 0, 1, 2,...?

Ackermann function

In a list of 4 positive even numbers, the mean, median and mode are all equal. Which of the following CANNOT be done to the list if the mean, median and mode are to remain equal?

Add one number to the list that is greater than the mean.

In a list of five integers, if the mode of the list is two less than the median, which of the following could be true?

The average (arithmetic mean) is less than the median.

All of the elements of list M and list N are arranged in exactly 20 pairs, such that every element from list M is paired with a distinct element from list N. If in each such pair, the element from list M is larger than the element from list N, then which of he following statements must be true?

The median of the elements in M is greater than the median of the elements in N.

The characteristic roots of a dynamic system are - 1.792 - j1.8160, - 1.7920 + j1.8160, - 0.4160. What is the damping ratio of the system?

1 or greater than 1

Which of the following statements with respect to the stability of a control system is NOT true?

The roots of the characteristic equation are on the left half of the s-plane and on the imaginary axis.

Consider a continuous-time system with input x(t) and output y(t) given by y(t) = x(t) cos (t). This system is ______.

linear and time-varying

The p-value in hypothesis testing represents:

The probability of obtaining the observed sample data or more extreme results, assuming the null hypothesis is true.

Given points P(1, -1, 0), Q(2, 1, - 1), and R(-1, 1, 2). Find a vector perpendicular to the plane formed by P, Q, and R.

- 6i + 6k

The divergence of the vector field A = xa_x + ya_y + za_z is:

1

In 2006, the number of home runs hit by each of the 16 National League teams us 88, 71, 75, 84 ,59, 71, 61, 59, 68, 54, 92, 60, 82, 66, 44 and 99. Find a 99% confidence interval for the mean number of home runs hit by National League teams.

(59.75, 81.87)

To check and see if a random number generator is working properly, twelve values from a unit normal distribution are generated. They are -0.5, -1.3, -0.7, 2.1, 0.1, 1.1, -0.2, 0.5, -0.2, -1.7, -0.9, and 1.6. What is the 95% confidence interval for the variance of this data set?

(0.6683, 3.8391)

The data below shows a sample of nine polishing times for bowls and their diameters. Find a 95% confidence interval for the slope of the regression line predicting polishing time based on bowl diameter.

(1.89, 2.77)

A couple has three children, and it is known that at least one of the children is a girl. What is the probability that the couple has at least one boy, assuming that having a boy or girl is equally likely?

0.857

The data below shows a sample of nine polishing times for bowls and their diameters. Find a 95% confidence interval for the intercept of the regression line predicting polishing time based on bowl diameter.

(-2.89, 4.73)

In a data set with n = 1292 it is found that x = $125,000 and the medians is $50,0000. Based on this information:

we can conclude that the data set is skewed on the right

A student wonders whether or not the grade point average for the junior year in college is different than the grade point average for the first year of college. She finds 10 students to give her their grade point average for their junior year and 10 other students to give her their grade point average for their first year of college. The data is in the table below. What is a 99% confidence interval for the mean difference of first year and junior year grade point averages?

(-0.913, 0.417)

A researcher is planning to do a hypothesis test with H₁: µ > µ₀. The test will be done with a level of significance of 0.05. it is desired that the test be able to detect a difference between µ₀ and µ₁, the actual population mean, of 1.77 and that the probability of a type II error be 0.15. Assume that the population standard deviation is 7.5. Approximately what sample size is necessary?

127

A sample of 23 plates has a mean polishing time of 32.12 minutes, and the process Is known to have a population standard deviation of 11.0 minutes. A sample of 37 cookware objects has a mean polishing time of 41.36 minutes, and the process is known to have a population standard deviation of 21.0 minutes. Find a 90% confidence interval for the difference in mean polishing time.

(-16.06, -2.42)

A large family owns five chickens. In the past, the five chickens laid an equal amount of eggs. Over the last four weeks the five chickens laid 34, 28, 16, 17, and 25 eggs each. Use a hypothesis test to determine if the chickens are still laying eggs in equal amounts. Based on the hypothesis test,

At the 0.05 but not at the 0.01 level of significance we conclude that the distribution has changed

The expense of moving a warehouse is justified only if it can be shown that the daily mean travel distance will be less than 250 miles. In trial run of 35 delivery trucks, the mean distance is 225 miles. The company assumes that σ = 45. What is a 96% confidence interval for the mean distance traveled?

(209.38, 240.62)

What is the geometric mean of the numbers 1 through 10?

4.53

Water is poured into a spherical tank at a constant rate. If W(t) is the rate of increase of the depth of the water, then W is:

Concave up