Evaluation of a probability using Markov's inequality

[Mishe Mitasek]

X,Y and Z are independent RVs with a MGF Mx(t)=1/(1−t).
How can I evaluate in the most efficient manner P(X+Y+Z>6)?

Thank you

 

[Dason]

Do you know what distribution that mgf belongs to? That's step one. The sum of three independent rvs with that distribution also make a known distribution.

 

[Dason]

Actually... Were you told to use markovs inequality? Because I guess you wouldn't explicitly need to figure out what distribution that is for if that's the case.

 

[katxt]

Do you know what distribution that mgf belongs to?

Exponential with rate 1, perhaps? So something to do with gamma. It's been so long....

 

[katxt]

In Excel type =1-GAMMADIST(6,3,1,1) ( I think... You're unlikely to get more efficient than that if it's true.)

 

[Dason]

This is almost definitely homework. Don't do all of their work for them. Plus my question is very relevant and although your approach is correct it probably isn't what their professor is going for.

 

[katxt]

OK, you're right. They still have to justify all the steps, and it seems unlikely to me that Markov's inequality will help here.

 

[Dason]

To get an exact answer it won't. But you can use the information provided to get what you need to put a bound on the probability even without identifying the distribution. So yeah... Let's see if they were instructed to use markovs inequality.