Statistics question (variance)

In summary: Here we have p(X,Y)=1/3. Then Var(X-2Y) = 9 + 4 - 12(1/3) = 13/3.In summary, we are asked to compute the variance of X-2Y, given that X and Y are random variables with a probability of 1/3, Var(X) = 9, and Var(Y) = 1. Using the formula Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y), we can substitute in our known values and get Var(X-2Y) = 9 + 4 - 4(1/3) = 13/3.
  • #1
hanelliot
18
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Studying for an intro course test and I have no one to compare it to right now.. any help would be appreciated.

Here is the question.

Q. Suppose X and Y are random variables such that p(X,Y)=1/3, Var(X) = 9 and Var(Y) = 1. Compute Var(X-2Y).

Since X and Y are not independent, we are using this formula: Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y), correct?
So, Var(X-2Y) = Var(X) - 4Var(Y) - 2Cov(X,Y)? How do I proceed from here?
 
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  • #2
hanelliot said:
Studying for an intro course test and I have no one to compare it to right now.. any help would be appreciated.

Here is the question.

Q. Suppose X and Y are random variables such that p(X,Y)=1/3, Var(X) = 9 and Var(Y) = 1. Compute Var(X-2Y).

Since X and Y are not independent, we are using this formula: Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y), correct?
So, Var(X-2Y) = Var(X) - 4Var(Y) - 2Cov(X,Y)? How do I proceed from here?
First you have the get the correct equation:

Var(X-2Y) = Var(X) + 4Var(Y) - 4Cov(X,Y)
You have Var(X) and Var(Y) already.
I'll assume that p(X,Y) is the correlation function. If so Cov(X,Y)=p(X,Y)(Var(X)Var(Y))1/2.
 

1. What is variance in statistics?

Variance is a measure of how spread out a dataset is. It tells us how much the data values deviate from the mean or average of the dataset.

2. How do you calculate variance?

Variance is calculated by taking the difference between each data point and the mean, squaring those differences, and then finding the average of those squared differences. This value is known as the variance.

3. What does a high variance indicate?

A high variance indicates that the data values are spread out over a larger range, meaning there is a lot of variability in the dataset. This could be due to outliers or a large range of values.

4. What is the difference between variance and standard deviation?

Variance and standard deviation are both measures of variability in a dataset. However, variance is the average squared difference from the mean, while standard deviation is the square root of the variance. Standard deviation is often preferred because it is in the same units as the original data.

5. How is variance used in statistical analysis?

Variance is used to assess the variability of a dataset and can help us understand the distribution of the data. It is also used in hypothesis testing and to calculate confidence intervals for the mean of a population.

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