 # Get help with college statistics

Recent questions in College Statistics Dolly Robinson 2021-11-03 Answered

### For continuous random variables X and Y with joint probability density function $$f(x,y)=\begin{cases}xe^{-(x+xy)} & x>0\ and\ y>0\\0 & otherwise\end{cases}$$ Find P(X>1 and Y>1). Trent Carpenter 2021-11-03 Answered

### The joint density of the random variables X and Y is given by $$f(x,y)=\begin{cases}8xy & 0\leq x\leq 1, 0\leq y \leq x\\0 & otherwise\end{cases}$$ Find the conditional density of X Find the conditional density of Y Suman Cole 2021-11-01 Answered

### Two random variables X and Y with joint density function given by: $$f(x,y)=\begin{cases}\frac{1}{3}(2x+4y)& 0\leq x,\leq 1\\0 & elsewhere\end{cases}$$ Find the marginal density of X. sanuluy 2021-11-01 Answered

### Assume that X and Y are jointly continuous random variables with joint probability density function given by $$\displaystyle{f{{\left({x},{y}\right)}}}={b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{\frac{{{1}}}{{{36}}}}{\left({3}{x}-{x}{y}+{4}{y}\right)}\ {\quad\text{if}\quad}\ {0}{<}{x}{<}{2}\ {\quad\text{and}\quad}\ {1}{<}{y}{<}{3}\backslash{0}\ \ \ \ \ {o}{t}{h}{r}{e}{w}{i}{s}{e}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}$$ Find the marginal density functions for X and Y . Efan Halliday 2021-10-30 Answered

### Compute the distribution of X+Y in the following cases: X and Y are independent Poisson random variables with means respective $$\displaystyle\lambda_{{{1}}}{\quad\text{and}\quad}\lambda_{{{2}}}$$. generals336 2021-10-28 Answered

### Suppose that the random variables X and Y have joint p.d.f. $$f(x,y)=\begin{cases}kx(x-y),0 Find the marginal p.d.f. of the two random variables. banganX 2021-10-28 Answered ### Suppose that X and Y are continuous random variables with joint pdf \(\displaystyle{f{{\left({x},{y}\right)}}}={e}^{{-{\left({x}+{y}\right)}}}{0}{<}{x}{<}\infty\ {\quad\text{and}\quad}\ {0}{<}{y}{<}\infty$$ and zero otherwise. Find P(X+Y>3) nitraiddQ 2021-10-28 Answered

### Random variable X and Y have the joint PDF $$f_{XY}(x,y)=\begin{cases}c,\ x\geq 0,y\geq 0,(x^{2}+y)\leq 1,\\0,\ \ \ \ \ otherwise \end{cases}$$ Find the marginal PDF $$\displaystyle{{f}_{{{Y}}}{\left({y}\right)}}$$. hexacordoK 2021-10-27 Answered

### Assume that X and Y are jointly continuous random variables with joint probability density function given by $$\displaystyle{f{{\left({x},{y}\right)}}}={b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{\frac{{{1}}}{{{36}}}}{\left({3}{x}-{x}{y}+{4}{y}\right)}\ {\quad\text{if}\quad}\ {0}{<}{x}{<}{2}\ {\quad\text{and}\quad}\ {1}{<}{y}{<}{3}\backslash{0}\ \ \ \ \ {o}{t}{h}{r}{e}{w}{i}{s}{e}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}$$ Find Cov(X,Y). generals336 2021-10-27 Answered

### Which of the following is nota condition for constructing a confidence interval to estimate the difference between two population proportions? A. The samples must be selected randomly. B. The data must come from populations with approximately normal distributions. C. When samples are taken without replacement, each population must be at least 10 times as large as its corresponding sample. D. The samples must be independent of each other. E. The observed number of successes and failures for both samples must be at least 10. bobbie71G 2021-10-27 Answered

### True or False? A Kruskal-Wallis test is used to compare a continuous outcome in more than two independent samples. CMIIh 2021-10-27 Answered

### Trucks are used in many configurations. Three common configurations are tractors with 1, 2, and 3 trailers. Accident statistics for these configurations in 2002 are listed below. Fatal U.S. Truck Accidents in 2002 by Configuration $$\begin{array}{|c|c|} \hline \text{Truck Configuration} & \text{Number of Registered Vehicles}&\text{Number of Accidents} \\ \hline \text{Tractor, 1 trailer}&150,000&2,889\\ \hline \text{Tractor, 2 trailers}&5,100&154\\ \hline \text{Tractor, 3 trailers}&200&1\\ \hline \end{array}$$ Assume these statistics represent simple random samples for each configuration. Which of the following would be the most, appropriate test to use to determine whether the populations for each configuration have the same rate of fatal accidents? A) One-sample proportion z-test. B) Two-sample proportion z-test C) Chi-square test for independence D) Chi-square goodness-of-fit test E) Chi-square test for homogeneity of proportions Chesley 2021-10-27 Answered

### At a research facility that designs rocket engines, researchers know that some engines fail to ignite as a result of fuel system error. From a random sample of 40 engines of one design, 14 failed to ignite as a result of fuel system error. From a random sample of 30 engines of a second design, 9 failed to ignite as a result of fuel system error. The researchers want to estimate the difference in the proportion of engine failures for the two designs. Which of the following is the most appropriate method to create the estimate? A one-sample z-interval for a sample proportion A A one-sample z-interval for a population proportion B A two-sample z-interval for a population proportion C A two-sample z-interval for a difference in sample proportions D A two-sample z-interval for a difference in population proportions Ernstfalld 2021-10-27 Answered

### Suppose you took random samples from three distinct age groups. Through a survey, you determined how many respondents from each age group preferred to get news from T.V., newspapers, the Internet, or another source (respondents could select only one mode). What type of test would be appropriate to determine if there is sufficient statistical evidence to claim that the proportions of each age group preferring the different modes of obtaining news are not the same? Select from tests of independence, homogeneity, and goodness-of-fit. Since we are interested in proportions, the test for homogeneity is appropriate. Since we are determining if the current distribution fits the previous distribution of responses, the goodness-of-fit test is appropriate. Since we can claim all the variables are independent, the test of independence is appropriate. abondantQ 2021-10-26 Answered

### Suppose that X and Y are independent rv's with moment generating functions $$\displaystyle{M}_{{{X}}}{\left({t}\right)}$$ and $$\displaystyle{M}_{{{Y}}}{\left({t}\right)}$$, respectively. If Z=X+Y, show that $$\displaystyle{M}_{{{Z}}}{\left({t}\right)}={M}_{{{X}}}{\left({t}\right)}{M}_{{{Y}}}{\left({t}\right)}$$. jernplate8 2021-10-26 Answered

### Consider two continuous random variables X and Y with joint density function $$\displaystyle{f{{\left({x},{y}\right)}}}={b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{x}+{y}\ {o}\leq{x}\leq{1},{0}\leq{y}\leq{1}\backslash{0}\ \ \ \ {o}{t}{h}{e}{r}{w}{i}{s}{e}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}$$ P(X>0.8, Y>0.8) is? Zoe Oneal 2021-10-26 Answered

### Which of the following statistics are unbiased estimators of population​ parameters? Choose the correct answer below. Select all that apply. A) Choose the correct answer below. Select all that apply. B) Sample variance used to estimate a population variance. C) Sample proportion used to estimate a population proportion. D) Sample mean used to estimate a population mean. E) Sample range used to estimate a population range. F) Sample standard deviation used to estimate a population standard deviation DofotheroU 2021-10-26 Answered

### A standard 3 sigma x-bar chart has been enhanced with early warning limits at plus-minus one sigma from the centerline . Three sample means in a row have plotted above the +1 sigma line . what is the probability of this happening if the process is still in control. Chesley 2021-10-26 Answered

### A random sample of $$\displaystyle{n}_{{1}}={14}$$ winter days in Denver gave a sample mean pollution index $$\displaystyle{x}_{{1}}={43}$$. Previous studies show that $$\displaystyle\sigma_{{1}}={19}$$. For Englewood (a suburb of Denver), a random sample of $$\displaystyle{n}_{{2}}={12}$$ winter days gave a sample mean pollution index of $$\displaystyle{x}_{{2}}={37}$$. Previous studies show that $$\displaystyle\sigma_{{2}}={13}$$. Assume the pollution index is normally distributed in both Englewood and Denver. (a) State the null and alternate hypotheses. $$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}};\mu_{{1}}{>}\mu_{{2}}$$ $$\displaystyle{H}_{{0}}:\mu_{{1}}{<}\mu_{{2}};\mu_{{1}}=\mu_{{2}}$$ $$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}};\mu_{{1}}{<}\mu_{{2}}$$ $$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}};\mu_{{1}}\ne\mu_{{2}}$$ (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. (c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to two decimal places.) (d) Find (or estimate) the P-value. (Round your answer to four decimal places.) (e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha? At the $$\displaystyle\alpha={0.01}$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the $$\displaystyle\alpha={0.01}$$ level, we reject the null hypothesis and conclude the data are statistically significant. At the $$\displaystyle\alpha={0.01}$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the $$\displaystyle\alpha={0.01}$$ level, we reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver. Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver. Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. (Round your answers to two decimal places.) lower limit upper limit (h) Explain the meaning of the confidence interval in the context of the problem. Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver. Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver. Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver. Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver. generals336 2021-10-26 Answered

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