Statistics: mean/expected value of an continuous distribution

In summary, the conversation is about finding the expected value of a given distribution, f(x) = 0,02x, between the range of 0 and 10. The correct method to calculate the expected value is by using the integral of x * f(x). There was an initial mistake in the calculation, but it was later corrected to the expected value of 6,67.
  • #1
davidhansson
8
0
So, the exercise is to find the expected value of following distribution: f(x) = 0,02x 0<x<10

answer in the book says 6,67

As far as I knowe, the expected value is calculated by the Integral of x * f(x) between 0 and 10, in this case!
It looks like this won't give the result 6,67!

what am I doing wrong?

thanks/ David
 
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  • #2
I'm not sure. The expected value is this integral:
[tex]
E(X) = \int_0^{10} x f(x) \, dx
[/tex]

What do you get when you evaulate it?
 
  • #3
davidhansson said:
So, the exercise is to find the expected value of following distribution: f(x) = 0,02x 0<x<10

answer in the book says 6,67

As far as I knowe, the expected value is calculated by the Integral of x * f(x) between 0 and 10, in this case!
It looks like this won't give the result 6,67!

what am I doing wrong?

thanks/ David

We cannot possibly help if you don't show us what you did in detail.
 
  • #4
oops, it's actually 6,67 as the book says,, it was just a computational mistake by me.

thank you anyways guys!

thanks/ David
 

1. What is the difference between mean and expected value in statistics?

The mean and expected value are both measures of central tendency in a continuous distribution. The mean is calculated by taking the sum of all data points and dividing by the number of data points, while the expected value is calculated by multiplying each data point by its corresponding probability and then summing the results. Essentially, the mean is a measure of what is most likely to occur, while the expected value takes into account the probability of each outcome.

2. Can the mean and expected value be the same in a continuous distribution?

Yes, in some cases the mean and expected value can be the same. This occurs when all data points in the distribution have the same probability. In this scenario, the expected value would be equal to the mean since each data point has an equal chance of occurring.

3. How is the mean or expected value affected by outliers in a continuous distribution?

The presence of outliers can significantly affect the mean, as it is heavily influenced by extreme values. However, the expected value is less affected by outliers since it takes into account the probability of each data point. In general, the expected value is a more robust measure of central tendency in the presence of outliers.

4. Can the mean or expected value be negative in a continuous distribution?

Yes, both the mean and expected value can be negative in a continuous distribution. This can occur when the data points are spread out in a way that results in a negative value when calculating the mean or expected value. It is important to consider the context of the data when interpreting negative values.

5. How can the mean or expected value be used in decision making?

The mean and expected value can be used to make predictions and inform decision making. In a continuous distribution, the mean and expected value can be seen as the most likely outcome, and this information can be used to make decisions or plan for future events. However, it is important to note that these measures of central tendency should be used in conjunction with other statistical tools and considerations to make well-informed decisions.

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