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(a) Compute descriptive statistics. (b) Perform a least-squares fit (optionally graph). (e) Determine the MLEs for the best fit from (b).


13.1 Complete data—failure times in days:

18.7 27.2 33.1 19.1 9.5 14.2 31.3 57.9

1.5 164.6 30.8 35.9 26.8

Answer :

Compute descriptive statistics: Find the mean, median, mode, range, and standard deviation of the data set. Perform a least-squares fit: Determine the best-fitting line that minimizes the sum of squared differences between observed and predicted values.

1. Mean: To find the mean, sum up all the values in the data set and divide the sum by the total number of values. For example, (18.7 + 27.2 + 33.1 + 19.1 + 9.5 + 14.2 + 31.3 + 57.9 + 1.5 + 164.6 + 30.8 + 35.9 + 26.8) / 13 =
2. Median: The median is the middle value in a sorted data set.
3. Mode: The mode is the value that appears most frequently
4. Range: The range is the difference between the highest and lowest values in the data set.
5. Standard Deviation: The standard deviation measures the dispersion or spread of the data

Performing a least-squares fit involves finding the best-fitting line that minimizes the sum of the squared differences between the observed data points and the predicted values. MLEs are estimators that maximize the likelihood function, which measures how likely the observed data is under the given model.

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