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Let x be a nilpotent element of the commutative ring R i.e. x^m for some positive integer m
a) Prove that x is either zero or a zero divisor
b)Prove that rx is nilpotent for all r in R
c)Prove that 1+x is a unit in R
d)Deduce that the sum of a nilpotent element and a unit is a unit
Fair die is rolled 10 times. Determine the probability that the odd number (1, 3 or 5) will occur less than 4 times?
The last lessons have spent a lot of time describing the slope and intercept terms (and their variances) of the one-variable sample regression function.
There are many nonparametric tests that have been developed over the years. Explain what nonparametric tests are and why they were developed.
If you know you need a sample size of 1,063 out of 300,000 to get a 95% confidence level and a 3% confidence interval what steps would you take to get a random sample?
If the interval of time between the eruptions is normally distributed with a standard deviation of 29 minutes, what is the probability that a randomly selected time interval between eruptions is longer than 96 minutes?
At one excavation site 8641 pot shards have been found that not yet been cleaned and identified. What is the probability that:
Kansas City prefer the new package, the probability that Catherine's random sample of 300 households will have a sample proportion greater than 0.45 is?
Calculate a 95 percent confidence interval for the population mean audit delay for all public owner-controlled companies in New Zealand.
Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. What is the value of the sample test statistic? (Round your answer to two decimal places.)
What are the assumptions of regression analysis and how do you evaluate them?
The time a cashier spends processing individual customer's order are independent random variables with mean 2.5 minute and standard deviation of 2.
Can we conclude from this that most workers there earn between $25 and $35 per hour? Is this right interpretation for margin of error?
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