Expected value of a continuous random variable

In summary, to find the expected value, E(x), for a PDF with two intervals, the integral can be divided into two integrals and then calculated using the formula E{X} = (1/12)*(integral of x from 0 to 3) + (1/18)*(integral of x^2 from 3 to 6). It is important to be careful with calculations to avoid errors.
  • #1
rayne1
32
0
Given the PDF:

f(x) = 1/12 , 0 < x <= 3
x/18, 3 < x <= 6
0, otherwise

find the expected value, E(x).

I know how to find the expected value if there was only one interval, but don't how to do it for two.
 
Physics news on Phys.org
  • #2
rayne said:
Given the PDF:

f(x) = 1/12 , 0 < x <= 3
x/18, 3 < x <= 6
0, otherwise

find the expected value, E(x).

I know how to find the expected value if there was only one interval, but don't how to do it for two.

The integral can be devided in two integrals as follows...

$\displaystyle E \{X \} = \frac{1}{12}\ \int_{0}^{3} x\ d x + \frac{1}{18}\ \int_{3}^{6} x^{2}\ dx\ (1)$

Kind regards

$\chi$ $\sigma$
 
Last edited:
  • #3
chisigma said:
The integral can be devided in two integrals as follows...

$\displaystyle E \{X \} = \frac{1}{12}\ \int_{0}^{3} x\ d x + \frac{1}{18}\ \int_{3}^{6} x^{2}\ dx\ (1)$

Kind regards

$\chi$ $\sigma$

Oh I did try that, so then I must have made a calculation error.
 

FAQ: Expected value of a continuous random variable

What is the expected value of a continuous random variable?

The expected value of a continuous random variable is a measure of the average value that can be expected from the variable over a large number of trials or observations. It is a weighted average of all possible values that the variable can take on, with the weighting factor being the probability of each value occurring.

How is the expected value of a continuous random variable calculated?

The expected value of a continuous random variable is calculated by multiplying each possible value by its corresponding probability of occurring, and then summing these products. This can also be expressed as the integral of the variable multiplied by its probability density function.

Why is the expected value of a continuous random variable important?

The expected value of a continuous random variable is important because it provides a way to summarize the behavior of the variable and make predictions about its future values. It also allows for comparison between different variables and can help in decision-making processes.

What is the relationship between expected value and variance?

Expected value and variance are both measures of central tendency and variability, respectively, for a continuous random variable. They are related in that the variance is a measure of the spread of the variable's values around its expected value. A higher variance indicates a greater spread, while a lower variance indicates a more concentrated distribution around the expected value.

Can the expected value of a continuous random variable be negative?

Yes, the expected value of a continuous random variable can be negative if the distribution of the variable is skewed to the left, meaning that there is a higher probability of lower values occurring. However, in most cases, the expected value is positive as it represents the average value of the variable.

Similar threads

I Statistical modeling and relationship between random variables
Replies
7
Views
2K
I Max of 3 random cards from deck vs max of 3 numbers from 1-13
Replies
5
Views
1K
I Sample space, outcome, event, random variable, probability...
Replies
6
Views
2K
I Linear regression and random variables
Replies
30
Views
3K
I Expected value of X~Geom(p) given X+Y=z
Replies
5
Views
993
MHB How to find PDF and Expected value of max(x,0), for a random variable x
Replies
1
Views
2K
I Is this conditional expectation identity true?
Replies
1
Views
928
I Sampling theory and random sample
Replies
5
Views
2K
I Random variable and elementary events
Replies
9
Views
2K
I How to obtain moment bound from the importance sampling identity?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top