probability distribution help please

Scroll to see replies

Is it like this?

Study Forum Helper

Original post by farhanaktar

Is it like this?

Nope. Refer back to how expectation is defined for a continuous random variable.

Study Forum Helper

Original post by farhanaktar

...

Thats also incorrect. Why are you integrating from -infinity ?? The pdf you use in the integrand is only valid for x>0.

And why are you omitting sigma ??

And again, you should look at how expectation is defined because you are not using the definition right now.

Is it 0 and 1 then

The integral values should be 0 and 2 then am I right sorry to disturb you

Do I have to include sigma then

Study Forum Helper

Original post by farhanaktar

Do I have to include sigma then

Of course, the original problem has it as a parameter!

Original post by farhanaktar

The integral values should be 0 and 2 then am I right sorry to disturb you

Alright enough guessing.

If

X

is a half normal distribution derived from the normal distribution with mean of zero and variance

\sigma^2

, then it has pdf of

Unparseable latex formula:

f(x) = \begin{cases} 0 & \text{if} \ x < 0 \\ \dfrac{2}{\sigma\sqrt{2\pi}}e^{-\frac{x^2}{2\sigma^2}} & \text{if} \ x\geq 0

.

Hence the expectation is given by

\displaystyle \int_{-\infty}^{\infty} xf(x).dx

but since

f(x) = 0

for

x<0

, this integral reduces to

\displaystyle \mathbb{E}[X] = \int_0^{\infty} x \dfrac{2}{\sigma\sqrt{2\pi}}e^{-\frac{x^2}{2\sigma^2}}.dx

which I will leave to you to calculate.

(edited 4 years ago)

OP

should I substitute 1 for the sigma and then makes it easier to integrate

Study Forum Helper

Original post by zulhaq345

should I substitute 1 for the sigma and then makes it easier to integrate

No

Is this fine and should I place sigma if you think is wrong.

Study Forum Helper

Original post by farhanaktar

Is this fine and should I place sigma if you think is wrong.

It's not fine because sigma is not necessarily 1.

I've made that clear in my previous comment yet you still made it 1 ?

Is this fine now I placed the sigma

OP

oh ok. sorry bro

Study Forum Helper

Original post by farhanaktar

Is this fine now I placed the sigma

It's fine at first and you got the right substitution... but the integral in

u

is incorrect. You need to replace

xdx

by the appropriate expression in

u

and

du

.

Would you mind circling the error please. I don't get it. Thank you do much for helping me out

Quick Reply

Latest

Trending

Trending

Articles for you

The Student Room Group Privacy Notice

What is an LLM and how could it benefit your career?

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Powerful questions business students forget to ask their career advisers

Why I chose a law degree and what studying law was like

Why I chose a law degree and what studying law was like