# 数据分析代考：Modelling for Data Analysis FIT2086

BA 通常需要将数据分析作为制定数据建模决策的一部分，这意味着数据建模可以包括一定数量的数据分析。使用非常基本的技术技能可以完成很多工作，例如运行简单数据库查询的能力。这就是为什么您可能会在业务分析师的职位描述中看到像 SQL 这样的技术技能。

## Modelling for Data Analysis FIT2086 数据分析代考案例

1.Maximum Likelihood Estimation

A random variable Yis said to follow an exponential distribution with a rate parameter β, if

P(Y=y|β) = βexp (−βy)

where y > 0 is a non-negative continuous number. Imagine we observe a sample of nnon-negative real numbers y= (y1, . . . , yn) and want to model them using an exponential distribution. (hint: remember that the data is independently and identically distributed).

1. Write down the exponential distribution likelihood function for the data y(i.e., the joint proba- bility of the data under an exponential distribution with rate parameter β).

2. Write down the negative log-likelihood function of the data yunder an exponential distribution with rate parameter β.

3. Derive the maximum likelihood estimator for β

2.Confidence Intervals and p-values: I

A car company runs a fuel efficiency test on a new model of car. They perform 6 tests, and in each test they drive the car until the fuel tank is empty, then calculate the litres of fuel consumed per one-hundred kilometers of distance covered. The observed efficiencies (in litres per 100 kilometers, L/100km) were:

y= (7.87,8.10,9.07,8.83,7.60,8.91).

From previous efficiency experiments the car company has estimated the population standard deviation in fuel efficiency recordings (i.e., the experimental error) to be 0.3 (L/100km). We can assume that a normal distribution is appropriate for our data, and that the population standard deviation of fuel efficiency recordings for our experiment is the same as the population standard deviation of fuel efficiency recordings of previous experiments.

1. Using our sample, estimate the population mean fuel effiency for this brand of car. Calculate a 95% confidence interval for the population mean fuel efficiency and summarise your results appropriately.

2. The car company runs the same set of tests, on the same set of cars, but with a different brand of fuel. The new observed fuel efficiencies (again, in L/100km) were

yB= (7.74,7.74,8.22,7.88,7.85,8.27). The company wants to know if this fuel has made any difference to the fuel efficiency. Again, we can assume the population standard deviation for this new set of fuel efficiency measurements is known to be 0.3L/100km. Using this information, please provide a p-value for testing the null hypothesis that the mean fuel efficiency for the two fuel types is the same. Please interpret this p-value.

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