# Probability of a (discrete) random variable

• Mar 8th 2012, 08:42 AM
snypeshow
Probability of a (discrete) random variable
I'm having trouble understanding this question:

Quote:

Suppose the random variable x = 1, 2, 3, 4, 5, 6.
p(1)=p(2) and p(3)=p(4)=p(5)=p(6)
If the mean μ=4.00, then P(2 ≤ x ≤ 3) is:
So since all the values of x are laid out, x is a discrete random variable. Since there are only really two distinct probabilities, I'm guessing this would be a binomial distribution.

The binomial distribution formula is: p(x) = nCx * px * (1-p)n-x

and since the mean is given, i know the mean = n*p, but I don't know how I'd find either n or p since neither are given

any ideas?
• Mar 8th 2012, 09:58 AM
Plato
Re: Probability of a (discrete) random variable
Quote:

Originally Posted by snypeshow
I'm having trouble understanding this question:
Suppose the random variable x = 1, 2, 3, 4, 5, 6.
p(1)=p(2) and p(3)=p(4)=p(5)=p(6)
If the mean μ=4.00, then P(2 ≤ x ≤ 3) is:

This is not binomial.
You have two probabilities $\displaystyle a~\&~b$.
From the given $\displaystyle 2a+4b=1$ and $\displaystyle 3a+18b=4$.
Solve for $\displaystyle a~\&~b$. The your answer is $\displaystyle a+b$
• Mar 8th 2012, 10:02 AM
snypeshow
Re: Probability of a (discrete) random variable
I understand how you got 2a and 4b, but how did you get 3a and 18b?
• Mar 8th 2012, 10:09 AM
Plato
Re: Probability of a (discrete) random variable
Quote:

Originally Posted by snypeshow
I understand how you got 2a and 4b, but how did you get 3a and 18b?

How does one find the mean(expected value) of a distribution?
• Mar 8th 2012, 10:18 AM
snypeshow
Re: Probability of a (discrete) random variable
Expected value is the sum of x multiplied by its probabilities

(1+2)a and (3+4+5+6)b

ok, so I understand that part, but why would you set it to equal 4.0 which is the standard deviation?
• Mar 8th 2012, 10:22 AM
Plato
Re: Probability of a (discrete) random variable
Quote:

Originally Posted by snypeshow
Expected value is the sum of x multiplied by its probabilities

(1+2)a and (3+4+5+6)b

ok, so I understand that part, but why would you set it to equal 4.0 which is the standard deviation?

$\displaystyle \text{The standard deviation }\ne\text{ the mean.}$
• Mar 8th 2012, 10:40 AM
snypeshow
Re: Probability of a (discrete) random variable
Oh, ok, I gotchya!! Thanks dude!!