Compute Variance of Random Variable X

In summary, the variance of a random variable X can be computed using the formula V(X) = sqrt(E((X-E(X))^2)), where E(X) is the expectation value of X. This formula can be simplified to V(X) = (E((X-E(X))^2))^(1/2). To find the variance, use parameter differentiation and the fact that E is a linear operator. However, without a clear understanding of probability and parameter differentiation, it may be difficult to solve this problem.
  • #1
cscott
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1

Homework Statement



Compute the variance of the random variable X given by

[tex]V(X) = \sqrt{E((X-E(X))^2)}[/tex]
where E(X) is the expectation value of random variable X

Homework Equations



Hint: Use parameter differentiation

The Attempt at a Solution



I have no idea what to do here. I've never taken a class in probability and I have never heard of parameter differentiation. I've seen definitions of variance the same as above minus the square root sign so I'm confused.
 
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  • #2
http://en.wikipedia.org/wiki/Variance

look at "Computational formula for variance"

hmm you should have no square root; the formula you have is the standard devation S(x)

S(x) = (V(x))^(1/2)

At least what I know of statistics.

Use that E is linear operator (E : expectation value)

But I must say that it is hard so see what is meant by the problem..
 
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What is the definition of variance?

Variance is a measure of how spread out a set of data points are from the mean. It is calculated by taking the average of the squared differences between each data point and the mean.

How is variance related to standard deviation?

Standard deviation is the square root of variance. It is a measure of the average amount by which data points deviate from the mean. In other words, variance measures the variability of the data, while standard deviation measures the spread of the data.

What is the formula for computing the variance of a random variable X?

The formula for computing the variance of a random variable X is Var(X) = E[(X - E[X])^2], where E[X] is the expected value of X.

What are some real-world applications of computing variance?

Computing variance is often used in statistics, finance, and quality control to analyze data and make predictions. For example, in finance, variance is used to measure the risk associated with an investment portfolio. In quality control, it is used to monitor the consistency of production processes.

How can computing variance be helpful in scientific research?

In scientific research, computing variance can help identify patterns and trends in data, as well as assess the reliability and significance of results. It can also be used to compare different groups or treatments in experiments and determine if there is a statistically significant difference between them.

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