Practice Math Statistics Problems and Master the Concepts

Prove that the reduced row echelon forms of the matrices $(\begin{matrix} 1 & 1 & 4 & 8 & 0 & - 1 & - 1 \\ 1 & 2 & 3 & 9 & 0 & - 5 & - 2 \\ 0 & - 2 & 2 & - 2 & 1 & 14 & 3 \\ 1 & 4 & 1 & 11 & 0 & - 13 & - 4 \end{matrix}) (\begin{matrix} 0 & - 3 & 3 & 1 & 5 \\ 0 & 1 & - 1 & 0 & 0 \\ 0 & 2 & - 2 & 0 & - 3 \end{matrix})$

are the two matrices.

The point of the reduced row echelon form is that the corresponding system of linear equations is in a particularly simple form, from which the solutions to the system $A X = C i n (4)$ can be determined immediately.

banganX 2021-03-08

The pathogen Phytophthora capsici causes bell pepper plants to wilt and die. A research project was designated to study the effort of soil water content and the spread of the disease in fields of bell peppers. It is thought that too much water helps spread the disease. The fields were divided into rows and quadrants. The soil water content (percent of water by volume of soil) was determined for each plot. An important first step in such a research is to give a statistical description of the data.

postillan4 2021-03-07

Give a counter example to the statement $E (X Y) = E (X) E (Y)$ implies
that X and Y are independent.

Zoe Oneal 2021-03-07

1. A drug is being tested in a chronic disease whose condition waxes and wanes over time. Which of the following study designs is most effective in evaluating the efficacy and safety of a new therapy
for this disease?
A. Retrospective Cohort
B. Case-Control
C. Prospective, Randomized, Active Control, Parallel Group Design
D. Prospective, Randomized, Active Control, Crossover Design

Ernstfalld 2021-03-07

Consider binary strings with n digits (for example, if n=4, some of the possible strings are 0011,1010,1101, etc.)
Let Zn be the number of binary strings of length n that do not contain the substring 000
Find a recurrence relation for Zn
You are not required to find a closed form for this recurrence.

Jason Farmer 2021-03-07

M. F. Driscoll and N. A. Weiss discussed the modeling and solution of problems concerning motel reservation networks in “An Application of Queuing Theory to Reservation Networks” (TIMS, Vol. 22, No. 5, pp. 540–546). They defined a Type 1 call to be a call from a motel’s computer terminal to the national reservation center. For a certain motel, the number, X, of Type 1 calls per hour has a Poisson distribution with parameter $λ = 1.7$ .
Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be:
a) exactly one.
b) at most two.
c) at least two.
(Hint: Use the complementation rule.)
d. Find and interpret the mean of the random variable X.
e. Determine the standard deviation of X.

opatovaL 2021-03-07

Population The resident population P (in millions) of the United States from 2000 through 2013 can be modeled by $P = - 0.00232 t^{3} + 0.0151 y^{2} + 2.83 t + 281.8, 0 \leq t \leq 13,$ where $t = 0$ corresponds to 2000.
(Source: U.S. Census Bureau)
Make a conjecture about the maximum and minimum populations of the United States from 2000 to 2013.
Analytically find the maximum and minimum populations over the interval.
The brief paragrah while comparing a conjecture with the minimum population was 281.8 million in 2000 and the maximum population was 316.1 million in 2013.
We need to calculate: The absolute extrema of the popullation $P = - 0.00232 t^{3} + 0.0151 y^{2} + 2.83 t + 281.8, 0 \leq t \leq 13$ over the closed interval [0, 13].

Tobias Ali 2021-03-07

The time between successive customers coming to the market is assumed to have Exponential distribution with parameter l.
a) If $X_{1}, X_{2}, \dots, X_{n}$ are the times, in minutes, between successive customers selected randomly, estimate the parameter of the distribution.
b) The randomly selected 12 times between successive customers are found as $1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, and 0.6$ mins. Estimate the mean time between successive customers, and write down the distribution function.
c) In order to estimate the distribution parameter with 0.3 error and $4 %$ risk, find the minimum sample size.

ka1leE 2021-03-07

The American Journal of Political Science (Apr. 2014) published a study on a womans

ddaeeric 2021-03-07

A parks and recreation department is constructing a new bike path. The path will be parallel to the railroad tracks shown and pass through the parking area al the point $(4, 5) .$ Write an equation that represents the path.

boitshupoO 2021-03-07

What is the difference between quantitative and qualitative data.

Nann 2021-03-07

In an experiment designed to study the effects of illumination level on task performance (“Performance of Complex Tasks Under Different Levels of Illumination,” J. Illuminating Eng., 1976: 235–242), subjects were required to insert a fine-tipped probe into the eyeholes of ten needles in rapid succession both for a low light level with a black background and a higher level with a white background. Each data value is the time (sec) required to complete the task.
$\begin{array}{|c|c|} \hline Subject & (1) & (2) & (3) & (4) & (5) &(6) & (7) & (8) & (9) \\ \hline Black & 25.85 & 28.84 & 32.05 & 25.74 & 20.89 & 41.05 & 25.01 & 24.96 & 27.47 \\ \hline White & 18.28 & 20.84 & 22.96 & 19.68 & 19.509 & 24.98 & 16.61 & 16.07 & 24.59 \\ \hline \end{array}$
Does the data indicate that the higher level of illumination yields a decrease of more than 5 sec in true average task completion time? Test the appropriate hypotheses using the P-value approach.

Tazmin Horton 2021-03-06

What connection exists between a quantitative data set's frequency or relative frequency distribution and a qualitative data set?

Emily-Jane Bray 2021-03-06

Are all infinite random variables necessary continuous?Explain.

usagirl007A 2021-03-06

Find the regression line using the given points.

Chesley 2021-03-06

A sample of 51 research cotton samples resulted in a sample average percentage elongation of 8.19 and a sample standard deviation of 1.45. Calculate a $95 %$ large-sample CI for the true average percentage elongation $μ$ (Round your answer to three decimal places.)

Tyra 2021-03-06

Based on a sample of 80 recent Masters graduates (40 male and 40 female), the following information was made available regarding their annual salaries. The standard deviation of salaries for the male graduates was $40,000 and that for the female graduates was $25,000.
a) For the male graduates, what is the probability of obtaining a sample mean salary within $10,000 of the population mean?
b) Consider the same question in (a) but for the female graduates. In which case, males or females, do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean? Why?
c) Suppose that the sample mean salary of females is $125,000. Develop a $95 %$ confidence interval estimate for the mean salary of all female graduates

Ernstfalld 2021-03-06

Qualitative data that cannot be ranked is called categorical, nominal
1. True
2. False

banganX 2021-03-06

Which statement best characterizes the definitions of categorical and quantitative data?
Quantitative data consist of numbers, whereas categorical data consist of names and labels that are not numeric.
Quantitative data consist of numbers representing measurements or counts, whereas categorical data consist of names or labels
Quantitative data consist of values that can be arranged in order, whereas categorical data consist of values that cannot be arranged in order.
Quantitative data have an uncountable number of possible values, whereas categorical data have a countable number of possible values.

Zoe Oneal 2021-03-06

To explain:Whether the samples are independent or dependent.

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