Variance and Expected Value Problem

In summary, a possible example of a random variable with a mean of 4 and a variance of 4 is B=A+4, where A is a random variable with a mean of 0 and a variance of 4. This satisfies the given properties of EX=4 and VAR(X)=4. Another example could be a binomial random variable with n=4 and p=0.5, which also has a mean of 4 and a variance of 4.
  • #1
dspampi
16
0
Give an example of a random variable (i.e. give the range of values it takes and its p.m.f.) with the following properties: EX = 4, VAR(X)=4. Now give an example of a random variable with a different p.m.f. than the first one you gave, but that still has EX = 4, VAR(X)=4.


So this means then E(X) = E(X^2) - (E(x))^2 right?
I'm not sure if this is the way I should approach the problem?
 
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  • #2
Not really. They just happen to equal the same number. What I would do is first find a random variable A with a mean of 0 and variance of 4. Then the variable B=A+4 will have a mean of 4 and a variance of 4.
 

1. What is variance and expected value?

Variance and expected value are two statistical measures used to describe the spread and central tendency of a data set, respectively. Variance measures how much the data points deviate from the mean, while expected value is the average value that is expected to be obtained in repeated trials of a random experiment.

2. How do you calculate variance and expected value?

To calculate variance, first find the mean of the data set. Then, for each data point, subtract the mean and square the difference. Finally, add up all the squared differences and divide by the total number of data points. To calculate expected value, multiply each possible outcome by its probability of occurring and add them all together.

3. What is the significance of variance and expected value in data analysis?

Variance and expected value are important measures in data analysis as they provide insight into the distribution and central tendency of a data set. They can help identify patterns and trends, and can be used to make predictions and draw conclusions about the data.

4. Can variance be negative?

No, variance cannot be negative. It is always a non-negative value, as it is the squared deviation from the mean.

5. How are variance and expected value related?

Variance and expected value are related in that they both provide information about the distribution of a data set. Expected value gives the average value that is expected to be obtained, while variance measures the spread of the data around the expected value. A higher variance indicates a wider spread of data points, while a lower variance indicates a more concentrated set of data points.

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