# Random Variable

If X is a Gamma random variable with parameters (n,1), approximately how large need n be so that .......

Answer:

(a) Using Chebyshev's inequality;

(b) the Central Limit Theorem

https://brainmass.com/statistics/central-limit-theorem/random-variable-chebyshevs-inequality-central-limit-theorem-29369

#### Solution Preview

Please see the attached file.

Solution. We use the following facts. If X is a Gamma random variable with parameter (n,1), then the expected value E(X) and variance Var(X) of X are

....(1)

Note. You can get the above result in any book for the probability theory.

So,

(a) By Chebyshev's inequality, we ...

#### Solution Summary

If X is a Gamma random variable with parameters (n,1), approximately how large need n be so that ..........

Answer:

(a) Using Chebyshev's inequality;

(b) the Central Limit Theorem

$2.19