# Basic Statistics

What are the probabilities of drawing the samples (-1,0), (1,-1), and (1,0)?

What are the probabilities of drawing the samples (-1,0), (1,-1), and (1,0)?

What are the values the sample mean, , can take:

What are the values the sample mean, , can take:

The legal maximum level of the carbon emissions is 20 (parts per million). Test the hypothesis that the population mean level of carbon emissions for this type of engine is 20, against the alternative hypothesis that the population mean is less than 20. Use a Type I error probability of 1%. What is the value of the test statistic?

The legal maximum level of the carbon emissions is 20 (parts per million). Test the hypothesis that the population mean level of carbon emissions for this type of engine is 20, against the alternative hypothesis that the population mean is less than 20. Use a Type I error probability of 1%. What is the value of the test statistic?

What is the covariance between X and Y?

What is the covariance between X and Y?

The sample covariance between X and Y is:

The sample covariance between X and Y is:

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