6. If $X_{1}, X_{2}, X_{3}$, and $X_{4}$ are (pairwise) uncorrelated random variables, each having mean 0 and variance 1 , compute the correlations of (a) $X_{1}+X_{2}$ and $-X_{2}+X_{3}$. (b) $X_{1}+X_{2}+X_{3}$ and $X_{3}+X_{4}$. CS. JG.083
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- There are instances where system error occurs which greatly affects the mechanics of the game. In the past, it was recorded that, on the average, one system error occurs in every 500 games. To know the chances of system error(s) occurring in Shawn’s game, poisson distribution should be used with average rate of occurrence equal to _____. With this, the probability that Shawn will experience no system error in the game is ____.A lot of 75 washers contains 6 defectives whose variability in thickness is unacceptably large. A sample of 10 washers is selected at random without replacement. a. Calculate the variance of (x)Suppose administrators at a large school district decide to institute mandatory study halls at their middle schools in an effort to boost their students' academic performance. After one year, a guidance counselor decides to test whether students' grade point averages (GPAs) have improved compared to the previous school year. The counselor selects a random sample of 40 eighth-graders from throughout the district who were also enrolled in the district for seventh grade. He records their GPAs for grades seven and eight, and for each student, calculates the difference between the two. The counselor's data is summarized in the given table. Variabledescription Samplemean Sample standarddeviation Standarderror estimate seventh grade GPA x¯= 2.64796 s=0.45763 SE=0.07236 eighth grade GPA x¯=2.78543 s=0.54764 SE=0.08659 difference (8th - 7th) x¯=0.13747 s=0.34586 SE=0.05469 The counselor plans to use this information to conduct a matched-pairs t‑test of the null hypothesis H0:μ=0…
- A random sample of 10 from population 1 had a variance of 3.600, while a sample of 15 from population 2 had a variance of 2.400. Test the hypothesis, at the 5% level of significance, that the two population variances are the same. State your conclusion as a sentence including the test statistic and the critical value.Suppose the network flow size is a normal random variable with parameter μ = 71 GBytes and σ = 2.5GBytes. What percentage of the flows are greater than 72 GBytes? Suppose flows that are greater than72 GBytes are classified as large flows. What percentage of the large flows are greater than 77 GBytes?There are instances where system error occurs which greatly affects the mechanics of the game. In the past, it was recorded that, on the average, one system error occurs in every 500 games. To know the chances of system error(s) occurring in Ella's game, Poisson distribution should be used with average rate of occurrence equal to ______. With this, the probability that Shawn will experience no system error in the game is _______.
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- In the past decade, two presidential elections in the United States have witnessedvery long wait times at precincts (voting stations) in states that ultimately decidedthe election (Florida in 2000 and Ohio in 2004).In Philadelphia as well, some voters complained about the long lines in someprecincts, with most complaints coming from precinct A. In 2004, the averagenumber of voters arriving at Precinct A was 35 per hour and the arrivals of voterswas random with inter-arrival times that had a coefficient of variation of 1 (CVa=1).Philadelphia deployed 1 voting machine in Precinct A. Suppose that each voterspent on average 100 seconds in the voting booth (this is the time needed to casther/his vote using a voting machine), with a standard deviation of 120 seconds.Q1. How long on average did a voter have to wait in line at precinct A in 2004 beforeentering a booth to cast her/his vote?Given the long wait times for Precinct A, the city of Philadelphia is thinking ofalternative solutions to…In the past decade, two presidential elections in the United States have witnessedvery long wait times at precincts (voting stations) in states that ultimately decidedthe election (Florida in 2000 and Ohio in 2004).In Philadelphia as well, some voters complained about the long lines in someprecincts, with most complaints coming from precinct A. In 2004, the averagenumber of voters arriving at Precinct A was 35 per hour and the arrivals of voterswas random with inter-arrival times that had a coefficient of variation of 1 (CVa=1).Philadelphia deployed 1 voting machine in Precinct A. Suppose that each voterspent on average 100 seconds in the voting booth (this is the time needed to casther/his vote using a voting machine), with a standard deviation of 120 seconds. Q3. Under Proposal 1, at precinct A, what would be the ratio of the average numberof people voting (at a booth) over the average number of people in the line(waiting)? Please show and explain this problem.To find out whether a new serum will arrest leukemia, 9 mice, all with an advanced state of the disease are selected. Five mice receive the treatment and 4 do not. Survival times, in years, from the time the experiment commenced are provided. At the .01 level of significance, can the serum be said to be effective. Assue the populations to be normally distributed with equal variances. Let sample 1 be the mice that recieved the treatment and sample 2 be the mice that did not receive treatment . State the null and alternative hypotheses. Survival times (yrs) Treatment 2.1 5.5 1.2 4.4 0.7 Non-treatment 1.9 0.6 2.6 3.3 Identify the critical region. Determine the test statistic State the proper conclusion.