Category Archives: probability mass function

Using a Mass Function

Posted on October 29, 2022 by | Comments Off on Using a Mass Function

Let \(X\) be a random variable with probability mass function

\(p(n) = \frac{1}{c^n}\quad \text{for } n=2,3,4,\cdots\)
and \(p(x)=0\) otherwise.

  1. Find \(c.\)
  2. Compute the probability that \(X\) is even.

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Posted in probability mass function, Series

A p.m.f. and expectation example

Posted on September 18, 2013 by | Comments Off on A p.m.f. and expectation example

Let \(X\) be a random variable with probability mass function

\[p(n) = \frac{c}{n!}\quad \text{for $\mathbf{N}=0,1,2\cdots$}\]

and \(p(x)=0\) otherwise.

  1. Find \(c\). Hint use the Taylor series expansion of \(e^x\).
  2. Compute the probability that \(X\) is even.
  3. Computer the expected value of \(X\)

[Meester ex 2.7.14]

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Posted in Expectations, probability mass function

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