Download Here are 10 questions that will help you prepare for the Statistics

Here are 10 questions that will help you prepare for the Statistics final
#1. Find the following probabilities
A. P [ X  0.3] if X has a negative exponential distribution with   1
B. P [ X  1.65] if X has a standard normal distribution
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C. P [ 1.25  X  1.65] if X has a normal distribution with   2 and   3
D. P [ X  0.3] if X has a Bernoulli distribution with p = 0.8
#2. Find the theoretical or population means for the following
A. Calculate E [ X ] when X has a negative exponential distribution with   4
B. Calculate E [ X ] when X has a Bernoulli distribution with p = .25.
C. Calculate E [Y ] when Y  X 1  X 2 and X 1 and X 2 have Bernoulli distibutions with p = 0.25
D. Calculate E [2 X  3] when X has a negative exponential distribution with   2
#3. Find the theoretical or population variances for the following
A. Calculate var [ X ] when X has a negative exponential distribution with   4
B. Calculate var [ X ] when X has a Bernoulli distribution with p = .25.
C. Calculate var [Y ] when Y  X 1  X 2 and X 1 and X 2 have Bernoulli distibutions with p = 0.25
D. Calculate var [3 X  2] when X has a negative exponential distribution with   3
#4. Suppose you have data on random variable X given by x: 1 4 2 5
A. Find the sample mean
B. Find the sample variance and sample standard deviation
C. Find the sample mean of Y  2 X  3
D. Find the sample variance and sample standard deviation of Y  2 X  3
#5. What are the steps in testing a hypothesis like Ho: ,   2 , where  is an unknown parameter in
a negative exponential distribution?
#6. Use the Central Limit Theorem to test H o : p  0.4 for a Binomial distribution where N = 100, the
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sample mean is equal to x  26 , and the sample variance is ˆ  12 .
#7. Use the Central Limit Theorem to test H o :   0.25 for a Negative Exponential distribution where
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N = 100, the sample mean is equal to x  7.3 , and the sample variance is ˆ  2.2 .
#8. Use the Central Limit Theorem to test H o :   2.5 for a Normal Distribution where
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N = 25, the sample mean is equal to x  4.3 , and the sample variance is ˆ  1.6 .
#9. Suppose we have data on x and y as x: 1 3 3 5 y: 3 1 2 0 . Now find the sample covariance of X and
Y and the sample correlation coefficient between X and Y .
#10. What is the difference between a normal distribution and a standard normal distribution?