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# Random Variables and Probability Axioms watch

1. A random variable X takes integer values n=0,1,... with the following probabilites:
, where C is a constant. Find the value of C
2. (Original post by bijesh12)
A random variable X takes integer values n=0,1,... with the following probabilites:
, where C is a constant. Find the value of C
Well you know the sum of the probabilites over all the possible values X can take is "1"

So you need to consider, 1= P(X=0) + P(X=1) + P(X=2) + ....

If you take out the factor of C, you're left with a well known series expansion.

If you don't recognize it, try a few basic ones you know.
3. So

And so :

I'm not sure how to deal with the infinite sum.

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4. Thanks I've understood how to do the summation bit. Taylor series for E^x

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5. (Original post by bijesh12)
I'm not sure how to deal with the infinite sum.
If I rewrite the sum as , where , does that help?
6. (Original post by DFranklin)
If I rewrite the sum as , where , does that help?
Yes thanks I've figured it out to be Taylor series for e^1/2. And therefore c= 1 / sqrt (e)

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