What is the definition of mean?

Thread starter badgerbadger
Start date Nov 12, 2009
Tags

Distribution Normal Normal distribution

In summary, "Normal distribution E(x)=U" refers to a probability distribution with a symmetrically distributed values around the mean (E(x)) represented by the symbol U. The mean of a normal distribution is calculated by dividing the sum of all values by the total number of values. The mean (E(x)) is important as it represents the central value and is used to measure the location and spread of the data. It also affects the shape of the distribution as the point of symmetry. A normal distribution can have a mean (E(x)) of 0, indicating an even distribution of values around 0.

Nov 12, 2009

badgerbadger

suppose that f(x) is the density function of a normal distribution with mean u and standard deviation sigma. show that u= intergral from -infinity->+infinity xf(x)dx

Physics news on Phys.org

Nov 13, 2009

HallsofIvy

Science Advisor

Homework Helper

Again, what is the definition of "mean"?

What is the meaning of "Normal distribution E(x)=U"?

Normal distribution refers to a probability distribution in which the values are symmetrically distributed around the mean (E(x)) and follow a bell-shaped curve. The value of the mean is represented by the symbol U.

How is the mean (E(x)) of a normal distribution calculated?

The mean of a normal distribution can be calculated by taking the sum of all values and dividing it by the total number of values in the distribution.

What is the significance of the mean (E(x)) in a normal distribution?

The mean (E(x)) is the central value of a normal distribution and is used to measure the location and spread of the data. It also represents the most probable or average value in the distribution.

How does the mean (E(x)) affect the shape of a normal distribution?

The mean (E(x)) is the point of symmetry in a normal distribution, meaning that the curve is centered around this value. As the mean changes, the curve shifts left or right, but remains symmetric.

Can a normal distribution have a mean (E(x)) of 0?

Yes, a normal distribution can have a mean (E(x)) of 0. This means that the data is evenly distributed around 0, with approximately half of the values falling above 0 and half falling below 0.