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rogo0034
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Homework Statement
Find the Mean and Variance of Random Variable Z = (5x+3)
Using data set:
&
The Attempt at a Solution
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Find the Mean and Variance of Random Variable Z = (5x+3)
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In summary, the conversation discusses finding the mean and variance of a random variable using a given data set and the use of a theorem and corollary. It is suggested to compute the value of E(X) and Var(X) in order to apply the theorems and corollary.
Find the Mean and Variance of Random Variable Z = (5x+3)
Using data set:
&
- #2
rogo0034
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Sorry the data set it so large, I've been trying to adjust it to no avail.EDIT: Fixed it, should be easier to view now
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Ray Vickson
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rogo0034 said:Homework Statement
Find the Mean and Variance of Random Variable Z = (5x+3)
Using data set:
Using:
&
The Attempt at a Solution
You have a very small table of x and f(x) values. What is stopping you from computing EX? Why don't you just compute EX, then use that value in the computation of Var(X) = sum f(x)*(x-EX)^2 ?
RGV
- #4
rogo0034
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They want us to use the theorem and corollary, any ideas? I'm not too savvy with this stuff yet.
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Ray Vickson
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rogo0034 said:
OK, so use the theorem and the corollary. Does the first theorem have E(X) in it? Do you know the value of E(X)? If not, you need to compute it. Does the second theorem have [itex] \text{Var}(X) = \sigma_x^2[/itex] in it? Do you know the value of Var(X)? If not, you need to compute it.
RGV
FAQ: Find the Mean and Variance of Random Variable Z = (5x+3)
What is the formula for finding the mean of a random variable Z = (5x+3)?
The formula for finding the mean of a random variable Z = (5x+3) is mean = 5 * mean of x + 3. This means that you multiply the mean of x by 5 and then add 3 to get the mean of Z.
How do you calculate the variance of a random variable Z = (5x+3)?
The formula for calculating the variance of a random variable Z = (5x+3) is variance = 25 * variance of x. This means that the variance of Z is 25 times the variance of x.
Can the mean and variance of Z be negative?
Yes, the mean and variance of Z can be negative. This can happen if the mean and variance of x are both negative. The formula for finding the mean and variance of Z takes into account the mean and variance of x, so if they are negative, the resulting mean and variance of Z will also be negative.
Is there a relationship between the mean and variance of Z?
Yes, there is a relationship between the mean and variance of Z. The variance of Z is directly proportional to the mean of Z, meaning that as the mean of Z increases, the variance of Z also increases. This relationship is described by the formula variance = 25 * variance of x.
Can you give an example of using the mean and variance formula for Z = (5x+3)?
Let's say we have a random variable x with a mean of 2 and a variance of 4. Using the formula for finding the mean and variance of Z, we can calculate the mean and variance of Z as follows:
Mean of Z = 5 * 2 + 3 = 13
Variance of Z = 25 * 4 = 100
So, the mean and variance of Z in this example would be 13 and 100, respectively.