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Results tagged with probability
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user 164396
A probability provides a quantitative description of the likely occurrence of a particular event.
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vote
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answer
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Mixture distribution PDF with discrete values
For example, imagine that a given random variable $\mathbb{X}$ takes values as follows:
\begin{equation}
\mathbb{X} = \begin{cases}
exp(1/\lambda),\quad \text{with probability}\,\, p\\
0, \quad \text{ … with probability}\,\, (1-p)
\end{cases}
\end{equation}
So, my guess for the expression of the PDF of $\mathbb{X}$ is:
\begin{equation}
f(x) = (1-p)\cdot \delta(x) + p\cdot \lambda e^{-\lambda\,x}
\end …
- 75
0
votes
Accepted
Mixture distribution PDF with discrete values
To sum up:
Yes, you can express it as:
\begin{equation}
f(x) = (1-p)\cdot \delta(x) + p\cdot \lambda e^{-\lambda\,x} \cdot H(x)
\end{equation}
Note that Heaviside step function has been included in …
- 75