STA261 - Quiz 1A
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STA261 - Quiz 1A
1. (4 points) The following data were generated from an N(u, 1) distribution by a student. Unfortunately, the student forgot which value of u was used, so we are uncertain about the correct probability distribution to use to describe the variation in the data.
|
-0.1 |
0.7 |
2.1 |
0.6 |
2.0 |
0.8 |
1.9 |
1.2 |
|
0.7 |
-0.8 |
0.4 |
1.3 |
0.6 |
0.3 |
2.5 |
1.5 |
Can you suggest a plausible value for u? Explain your reasoning. Solution: We use the sample average 
= 0.98125. We base this on the weak law of large numbers because we know that 
will be close to u when n is large.
2. (6 points) Suppose that (z1 , . . . , zn ) is a sample from an N(u, 72 ) distribu- tion with 9 = (u, 72 ) e R1 x R+ unknown where R+ = (0, o). Suppose we parameterize the model by (u, ln 7) = (u, w). Record the statistical model using this parameterization, i.e., record the density function using (u, w) as the parameter and record the relevant parameter space.
Solution:
1. (4 points) The following data were generated from an N(u, 1) distribution by a student. Unfortunately, the student forgot which value of u was used, so we are uncertain about the correct probability distribution to use to describe the variation in the data.
|
1.3 |
1.8 |
-0.2 |
-0.1 |
1.2 |
0.8 |
3.0 |
2.8 |
|
0.1 |
3.0 |
2.6 |
0.1 |
0.0 |
1.0 |
0.6 |
-0.1 |
Can you suggest a plausible value for u? Explain your reasoning. Solution: We use the sample average 
= 1.11875. We base this on the weak law of large numbers because we know that 
will be close to u when n is large.
2. (6 points) Suppose it is known that a response X is distributed N(u, 72 ), where 9 = (u, 72 ) e R1 x R+ unknown where R+ = (0, o). Show how to calculate the first quartile of each distribution in this model from the values (u, 72 ). Is it possible to parameterize the model by the first quartile? Explain your answer.
Solution:
2022-02-16