Central limit theorem and exponential distribution

[Aedrha2]

Hello! I am currently studying a course in statistics and probability. Due to current restrictions alot of the education is online.

There is an assigment a check that we understand the basic theory, in which we are supposed to pair up random varibles with the right approximative distridution using th central limit theory.
The assignment reads:

"36 random varibles [imath]X_1,....,X_{36}[/imath] are independant and exponentially distributed with [math]E(X_i)=2[/math] and [imath]V(X_i)=4[/imath]. Pair up the random varibles and the approximative distribution."

I got all of them besides one:

[imath]X_{26}[/imath] and [imath]Exp(0.5)[/imath]

I've read through the text book and I don't understand how this connection is made.

What I've got is : [imath]X\in Exp(a), E(X)=a[/imath] and [imath]V(X)=a^2[/imath]

I can't connect the dots here, can someone help me out?

Thanks!

 

[Dr.Peterson]

Hello! I am currently studying a course in statistics and probability. Due to current restrictions alot of the education is online.

There is an assigment a check that we understand the basic theory, in which we are supposed to pair up random varibles with the right approximative distridution using th central limit theory.
The assignment reads:

"36 random varibles [imath]X_1,....,X_{36}[/imath] are independant and exponentially distributed with [math]E(X_i)=2[/math] and [imath]V(X_i)=4[/imath]. Pair up the random varibles and the approximative distribution."

I got all of them besides one:

[imath]X_{26}[/imath] and [imath]Exp(0.5)[/imath]

I've read through the text book and I don't understand how this connection is made.

What I've got is : [imath]X\in Exp(a), E(X)=a[/imath] and [imath]V(X)=a^2[/imath]

I can't connect the dots here, can someone help me out?

Thanks!

It might be helpful if you showed the whole problem, so we could see all the random variables they are asking about.

From what you say, each of the 36 random variables [imath]X_1,....,X_{36}[/imath] has the same distribution, which is exponential and [imath]E(X_i)=2[/imath] and [imath]V(X_i)=4[/imath]. Just from the expected value you can determine the parameter of the exponential distribution, [imath]\lambda[/imath], which is indeed 1/2. But what you say here suggests you have a different definition than what I find, for example, here:

Exponential distribution - Wikipedia

en.wikipedia.org

which says that [imath]E(X)=\frac{1}{\lambda}[/imath].

Can you show us what you were taught about this?

 

[Aedrha2]

@Dr.Peterson

You were indeed correct. Our text book only included the scale parameter. But the exercise material is from a diffrent source, which used the rate parameter in this case.

Looking at the link you provided solved my quandary almost instantly.

Thanks a bunch!

 

[Dr.Peterson]

@Dr.Peterson

You were indeed correct. Our text book only included the scale parameter. But the exercise material is from a different source, which used the rate parameter in this case.

Looking at the link you provided solved my quandary almost instantly.

Thanks a bunch!

That's yet another reminder that notation in math is not universal, so caution is always needed in combining different sources. And problems, whenever they might be taken out of context, should always define their terms.

I worry about students who try to learn from random videos or other online sources, rather than from one consistent textbook.