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# 统计exam代考 Statistics I代写 考试助攻 数据统计代写

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## Statistics I

Be reminded to define all random variables and relevant concepts. Justify your answers carefully. QUESTIONS MAY BE PRINTED ON THE BACK PAGES.

### RULES统计exam代考

➢ You are allowed to use a calculator.

➢ You are allowed to resort to printed documents and/or books.

➢ You are NOT allowed to use any electronic device besides your calculator. Your exam will be annulled if this rule is violated.

➢ You are NOT allowed to leave the room during the first 30 minutes after the beginning of the exam, except in case of sudden indisposition. You are allowed to leave after 30 minutes after handing in your exam.

### 1.

An analysis was conducted regarding the annual number of applications for patents in Portugal. The data were segmented by type of applicant: Universities, Companies, Research Institutes and Private Individuals. The results below encompass a period of 25 years:

(1,0) a) Fill the frequency table “Applications submitted by RESEARCH INSTITUES” by finding values (a-h).

(1,0) b) Indicate and interpret the median and the standard deviation of the number of patents submitted by UNIVERSITIES.

(0,5) c) Match each boxplot (A, B, C, D) with the respective type of applicant.

(1,5) d) State the logical value (True or False) of the statements below. Justify your answers.

i. The number of applications submitted by COMPANIES was greater than or equal to 33 in 25% of the yearly periods under analysis.

ii. The annual average number of applications submitted by RESEARCH INSTITUTES was 5,92.

iii. The number of applications submitted annually by COMPANIES exhibits a distribution with negative skewness and leptokurtosis.

### 2. 统计exam代考

Daily sales of hard drives of brands X and Y, at a computer hardware store, exhibits the following joint probability function (Y in rows, X in columns):

(0,5) a) Obtain the marginal distribution of X.

(0,75) b) Calculate the probability of X being the brand with the most sales on a given day.

(0,5) c) Calculate the proportion of days in which the sales of hard drives of brands X and Y are equal.

(0,75) d) Obtain the probability function of X, when exactly one hard drive of brand Y is sold.

(1,5) 3. Let X be a random variable with standard deviation 10×(3-1/2) and the following cumulative distribution function:

Calculate values k1 and k2 assuming that the probability of X exceeding 15 is equal to 0,75.

### 4.

The annual gross salary (in hundreds of EUR) for a certain role at a company is a random variable with the following probability density function:

Consider the employees with the aforementioned role:

(0,5) a) Calculate the probability of an employee picked at random having an annual gross salary greater than 42.000 EUR

(1,0) b) Calculate the largest annual gross salary among the bottom 5% earners.

Note: if you have not solved question a), assume that the random variable follows a Normal distribution with µ = 400 and σ = 80.

(1,5) c) Calculate the probability of an employee picked at random paying less than 49 hundred EUR in state contributions, provided that these contributions represent 20% of the annual gross salary.

(1,5) d) Calculate the probability of, out of 100 employees picked at random, there being less than 3 with an annual gross salary greater than 49.000 EUR.

### 5. 统计exam代考

The number of vaccines of brand Hope produced per second is a random variable that follows a Poisson distribution.

(1,0) a) In order to estimate the expected value of that population, the following random sample was obtained:

(x1, x2, x3, x4, x5, x6) = (10, 9, 11, 15, 7, 14)

(0,75) c) Calculate P[T > 25] if and .

### 7. 统计exam代考

The following statistics were proposed to estimate the mean of a sample of size 3, obtained from an Exponential population.

(0,75) a) Which of the above estimators are biased, if any?

(1,25) b) Obtain the relative efficiency of estimators T2 and T3. Which of these two estimators is the most efficient?

(0,75) c) Comment on the sufficiency of each of the four estimators.

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