Complete the patterns 0.02 0.2 blank 20 blank blank
2 answers:
The Complete pattern is; 0.02, 0.2, 2, 20, 200, 2000
<h2>Further Explanation;</h2><h3>Sequence</h3>- A sequence refers to a set of numbers, called terms, arranged in some particular order.
- There are two major types of sequences.
Arithmetic sequence
- An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference (d).
For example;
2,4,6,8,10,12,.............. is an arithmetic sequence with a common difference of 2.
- The nth term of an arithmetic series is therefore given by;
Where is the first term and d is the common difference.
- A geometric sequence is a sequence with the ratio between two consecutive terms constant.
- The sequence follows a pattern where the next term is found by multiplying by a constant called the common ratio, r.
For example;
0.02, 0.2, 2, 20, 200, 2000, ........... is a geometric sequence in which the common ratio is 10.
The nth term of a geometric sequence is given by;
where is the first term and r is the common ratio
Key words: sequence, arithmetic sequence, geometric sequence, common difference, common ratio
<h3>Learn more about;</h3>- Arithmetic sequence: brainly.com/question/11718753
- Geometric sequence: brainly.com/question/9300199
- Example of a geometric sequence: brainly.com/question/10601401
Level: High school
Subject: Mathematics
Topic: Sequence and series
Sub-topic: Geometric sequence
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Answer:
a)
For this case the value for is always smaller than the value of a, assuming
So then for this case it cannot be unbiased because an unbiased estimator satisfy this property:
and that's not our case.
b)
Since is a negative value we can conclude that underestimate the real value a.
c)
And assuming independence we have this:
e) On this case we see that the estimator is better than
and the reason why is because:
and that's satisfied for n>1.
Step-by-step explanation:
Part a
For this case we are assuming
And we are are ssuming the following estimator:
For this case the value for is always smaller than the value of a, assuming
So then for this case it cannot be unbiased because an unbiased estimator satisfy this property:
and that's not our case.
Part b
For this case we assume that the estimator is given by:
And using the definition of bias we have this:
Since is a negative value we can conclude that underestimate the real value a.
And when we take the limit when n tend to infinity we got that the bias tend to 0.
Part c
For this case we the followng random variable and we can find the cumulative distribution function like this:
And assuming independence we have this:
Since all the random variables have the same distribution.
Now we can find the density function derivating the distribution function like this:
Now we can find the expected value for the random variable Y and we got this:
And the bias is given by:
And again since the bias is not 0 we have a biased estimator.
Part e
For this case we have two estimators with the following variances:
On this case we see that the estimator is better than
and the reason why is because:
and that's satisfied for n>1.