Consider the joint probability distribution below:

Prob. (X=Xiand Y=Yi)	X	Y
0.15	4	20
0.35	-4	12.5
0.5	0	23

Compute the expected value for random variable X. (Report your answer with decimal precision. Make sure that you round up your answer to two decimal points.)

Compute the covariance between random variables X and Y. (Report your answer with decimal precision. Make sure that you round up your answer to two decimal points.

Suppose that X and Y are measured in dollars. The covariance is measured in:

Group of answer choices

dollar-squared, a meaningless unit

square-root of dollar, a meaningless unit

no units (varies between -1 and +1)

dollars

Compute the coefficient of correlationbetween random variables X and Y. (Report your answer with decimal precision. Make sure that you round up your answer to two decimal points.)

Suppose that X and Y are measured in dollars. The coefficient of correlation is measured in:

Group of answer choices

square-root of dollar, a meaningless unit

dollar-squared, a meaningless unit

dollars

no units (it varies between -1 and 1)

Y~N(45,900); i.e., Y is distributed normally with its mean being equal to 45 and its variance being equal to 900 (thus: standard deviation=30).

Prob.(Y<=32.5)=?

Report your answer in decimal precision. Round it up to two decimal points.

Y~N(45,900). Compute: Prob.(Y>75)

Report your answer in decimal precision. Round it up to two decimal points.

Y~N(45,900). Compute: Prob.(45

Report your answer in decimal precision. Round it up to one decimal points.

Y~N(45,900). Also, Prob.(Y<=Y*)=10%. What is Y*?

Report your answer in decimal precision. Round it up to two decimal points.

Consider a large population made of 1,000,000 observations (N=1,000,000). From this population, we choose 5,000 samples (with replacement). Each sample is of size 144 (n=144). Every time that a sample is selected, we compute the mean and we record it in a dataset. Ultimately, we end up with 5,000 samples. Central Limit Theorem implies that:

Group of answer choices

the population is normally distributed only if the obtained sample means are normally distributed.

the obtained sample means are normally distributed only if the population is normally distributed.

the obtained sample means are normally distributed.

the population is normally distributed.

The standard deviation of sampling distribution of means is called: the standard error. Compute the standard error, considering the information in the above question and assuming that population standard deviation is equal to 24. (Only report the numerical value of the standard error. Round up your answer to two decimal points).

Consider the information in the last two questions. What percentage of sample means are less than 97.5, assuming that the population mean is equal to 100? (Report your answer in decimal precision (rather than percentages). Round up your answer to two decimal points).

Consider the information in the last three questions. What percentage of sample means are greater than 97.5 yet less than 100? (Report your answer in decimal precision (rather than percentages). Round up your answer to two decimal points).