Question

I need help with an integral used to find probability/density function :)

Answer 1

The density function for the number of times the riders scream on a roller coaster is given by \[f(x)=\frac{ 1 }{ 10\pi }(1-\cos(2x))\] if 0<x<10pi and f(x)=0 otherwise

Answer 2

I need to find the mean number of screams over the course of the ride

Answer 3

so you just need to integrate this over that interval and divide by the total distance?

Answer 4

nvm i think all u have to do is integrate

Answer 5

I think so.... I tried looking at an example from my notes in class but I'm a little confused and don't remember why he set it up the way he did. From the notes he had he had a problem that wanted the mean and so he set it up to be \[\int\limits_{0}^{\infty}t f(t)dt\]

Answer 6

I don't get why he put the random t infront of the function though.... ?

Answer 7

ok i think we have same diffculty lol we dont understand question properly

Answer 8

does that function tell you the number of screams by the people on the roller coaster at x right

Answer 9

by saying t f(t) that means that function shows the number of ppl screaming / time at a given point

Answer 10

then by doing t f(t) you know how many have screaming at that infentesimal small dt so you integrate over all the time adding up all the small increments

Answer 11

The example from class had the piecewise function \[\frac{ 1 }{ 10 }e ^{-\frac{ t }{ 10 }} \] for if t is greater than zero. and f(t) = 0 everywhere else. He wanted to find the mean amount of wait time (the function is time spent waiting in line) and so he did \[\frac{ 1 }{ 10 } \int\limits_{0}^{\infty}te ^{-\frac{ t }{ 10 }}dt\]

Answer 12

ok ya that makes sense

Answer 13

sweet :) can you explain why please? :)

Answer 14

just do that intergral of x f(x) dx
and i think u might have to use the cos addition identinity

Answer 15

Yeah, I know how to solve it, I'm just confused about why the x is stuck infront of the f(x)

Answer 16

for your function \[\int\limits_{?}^{?} x f(x) dx\]x F(x) x is there because

Answer 17

xF(x) is giving you the actual number of screams at that point

Answer 18

because you know like the probability density function is just 1 when you integrate it from -inf to inf right

Answer 19

oh I see, okay that makes sense. Thanks :)

Answer 20

np :) we just have trouble cuz we dont understand the question

Answer 21

i had to look up what a probability density function was lol