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Let X1 , X2 , ⋯, XN be a random sample of size n from normal distribution with mean µ and variance σ2 . a). Find the maximum likelihood estimator of σ2 2 . (2 points) b). Find the asymptotic distribution of the maximum likelihood estimator of σ2 2 obtained in part (a).
- If a random sample of 38 public elementary schools is selected , what is the probability
That the number of students enrolled is will be more than 400 ?
In a shipment of 30 computers, 4 are defective. Four computers are randomly selected and tested. What is the probability that all four are defective if the first, second, and third ones are not replaced after being tested?
According to last year’s report, a filipino household spends an average of P400/day for food. Suppose you took a sample of 25 households. You determined how much each household spent for the food daily and the results revealed a mean of P380 and a standard deviation of P21.50. with 99% confidence what would be your conclusion
Due to ASF issue it was aired that the average price of a kilo of pork in MM is P195.00. However, a sample of 15 prices randomly collected from different markets in MM showed an average of P200.00 and with standard deviation of P9.50. using 0.05 significant level. What would be your conclusion for the price of pork in MM.
The mean score of the first periodic exam in Statistics is 89 and the standard deviation is 12. One student believed that the mean was less than this, she then randomly selected 34 students and computed their mean score. She obtained that the mean score of 85 at 99% confidence. Test the student belief. Use both method to evaluate
given: random sample of size n= 2 are drawn from a finite population consisting of the numbers 5,6,7,8, and 9
- How many possible samples are there
- List all the possible samples and the corresponding mean for each sample.
- Construct the sampling distribution of the sample means.
- Construct the histogram for the sampling distribution of the sample mean.
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(B) Internet service providers (ISP) need to resolve customer problems as quickly as possible. The probability for a customer call regarding Internet service interruption is resolved within one hour is 70%. During one day, the company had 10 customer calls. (10 marks)
a) What is the probability that exactly four of the customers had their problems solved? (Round your answer to the nearest thousandth).
Determine the number of different samples of the given size n that can be drawn from the given population of size of N
- Population (N)
1.7
2.10
3.12
4.56
5.70
6.15
7.30
8.9
9.7
10.20- Sample Size (n)
1.3
2.2
3.5
4.4
5.6
6.2
7.6
8.3
9.2
10.5- Number of Possible Samples
1.?
2.?
3.?
4.?
5.?
6.?
7.?
8.?
9.?
10.?1. It is the inequality in the alternative hypothesis when the keyword at most is used.
2. It is the inequality in the alternative hypothesis when the keyword at least least is used.
3. It is done to the level of significance when not equal is used in the alternative hypothesis.
