What are the values of a and b for the given density function if E(X)=-1?

[snoggerT]

Density Function and E(x)[solved]

The density function of X is given by

https://webwork.math.lsu.edu/webwork2_files/tmp/equations/48/83b2bf602cc895a007a673a9a23c3c1.png

If the expectation of X is E(X)=-1, find a and b.

The Attempt at a Solution

I'm actually working ahead of the class with this problem, so the material hasn't been covered, but I would like to figure it out. I know the equation for E(X), but don't know how to relate it to this problem. Please help.

E(X)=∫xf(x)dx

 

[LCKurtz]

You have two unknowns a and b, and you are given two conditions. f(x) is a density so what does that tell you? And you know E(x) value. Write down those two equations and solve for the unknowns a and b.

 

[snoggerT]

You have two unknowns a and b, and you are given two conditions. f(x) is a density so what does that tell you? And you know E(x) value. Write down those two equations and solve for the unknowns a and b.

- I haven't been able to figure it out with what you said. I know that the probability density function equation is the integral from a to b of f(x)dx, but I'm not sure how to relate that to the E(X) formula.

 

[LCKurtz]

- I haven't been able to figure it out with what you said. I know that the probability density function equation is the integral from a to b of f(x)dx, but I'm not sure how to relate that to the E(X) formula.

No. The probability density function is not "the integral from a to b of f(x)dx". The probability density function is f(x). But what do you know about probability density functions and their integrals? That will give you one equation in a and b. And the integral for E(x) = -1 will give you another.

 

[HallsofIvy]

You must have
$$\int_0^1 xf(x)dx= E(x)$$
and
$$\int_0^1 f(x) dx= 1$$

Actually do those integrals with f(x)= a+ bx and solve the two equations for a and b.

 

[snoggerT]

You must have
$$\int_0^1 xf(x)dx= E(x)$$
and
$$\int_0^1 f(x) dx= 1$$

Actually do those integrals with f(x)= a+ bx and solve the two equations for a and b.

- Thanks. I wasn't quite grasping what i was being told at first, but as soon as you put both equations up, I knew what to do.