intergration

im trying to intergrate the following probability function to find the expectation of the random variable

f(t)= 24/ 7t^4 1<= x < = 2

but i keep getting the wrong answer could someone go through it for me? thanks alot

Reply 1

El Stevo

you multiply it all by t first?

Reply 2

Gemini

I'm not sure what a probability function, but when I integrated it I got: -8/(7t^3)

You've got to be careful not to make it t^5 underneath. Where did the x come from?

Reply 3

El Stevo

f(t)= 24/7t^4
f(t)= (24/7)(t^-4)
to find the expectation, mulitply by t and then integrate
E(t)= Int [1,2] (24/7)(t^-3)

Reply 4

El Stevo

Gemini

I'm not sure what a probability function, but when I integrated it I got: -8/(7t^3)

You've got to be careful not to make it t^5 underneath. Where did the x come from?

when you are finding the expectation of a probability function via integration, you have to multiply the function by t before integrating it...

Reply 5

Gemini

Ok ...I admit I know nothing about Stats :smile:

So why *do* you have to multiply it by t then?

Reply 6

El Stevo

why? je ne quite sais pas... but to make it more confusing, if you want to work out the variance, you multiply the original expression by t^2 and then do the integration...

Reply 7

sarah12345

El Stevo

f(t)= 24/7t^4
f(t)= (24/7)(t^-4)
to find the expectation, mulitply by t and then integrate
E(t)= Int [1,2] (24/7)(t^-3)

when i did that i got

Int[2,1] 24 ln (7t^3)

but when i do this i get the wrong answer what have i done wrong?

Reply 8

material breach

El Stevo

why? je ne quite sais pas... but to make it more confusing, if you want to work out the variance, you multiply the original expression by t^2 and then do the integration...

The mean is the probability multiplied by the number of values the random variable can assume. Its a denifition I think. Tho I admit my fallability now so if there are some proper maths geeks out there who can correct the physicst go ahead.

Reply 9

Gauss

Gemini

Ok ...I admit I know nothing about Stats :smile:

So why *do* you have to multiply it by t then?

The definition of E(t) is the integral (assume its a continuous distribution) of t multiplied by the probability densitiy function. It's simply a definition.

Thus, if you were looking to find E(t^2) you integrate t^2 multiplied by the probability densitiy function.

In general, E_f(t)[x] = INT [x.f(t)].

Euclid.

Reply 10

sarah12345