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Probability Density Functions

How do you manipulate a probability density function?

I.e How do you find the mean, E(x) and Var(x) for a variable x? Is E(x) just integrating xf(x), and is this the same as the mean?

Thanks
Original post by HashBrowns
How do you manipulate a probability density function?

I.e How do you find the mean, E(x) and Var(x) for a variable x? Is E(x) just integrating xf(x), and is this the same as the mean?

Thanks


Yes E(X) = integral of (xf(x)) dx between the limits of f(x)
Var (x) = integral of x^2 f(x) dx - (E(x))^2 between the limits of f(x)

E(x) is the 'expected value' of X, which is essentially the mean
(edited 10 years ago)
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kachu
Original post by Barcelona'99
Yes E(X) = integral of (xf(x)) dx between the limits of f(x)
Var (x) = integral of x^2 f(x) dx between the limits of f(x)

E(x) is the 'expected value' of X, which is essentially the mean


For Var(x) you also need to subtract E(x)^2.

So Var(x) = ∫x2f(x)dx−(∫xf(x)dx)2 \int x^2 f(x)dx - (\int xf(x) dx)^2 with the appropriate limits.
Original post by kachu
For Var(x) you also need to subtract E(x)^2.

So Var(x) = ∫x2f(x)dx−(∫xf(x)dx)2 \int x^2 f(x)dx - (\int xf(x) dx)^2 with the appropriate limits.


haha yes, don't know why I forgot that! Thanks

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