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In probability theory, the characteristic function of a random variable is a complex-valued function that describes the distribution of that variable. In LaTeX, the characteristic function can be represented using the command \varphi
or \phi
.
In probability theory, the characteristic function of a random variable is a complex-valued function that describes the distribution of that variable. In LaTeX, the characteristic function can be represented using the command \varphi
or \phi
.
To write the characteristic function in LaTeX, use the following command:
$$
\varphi_X(t) = \mathbb{E}[e^{itX}]
$$
$$ \varphi_X(t) = \mathbb{E}[e^{itX}] $$
This represents the characteristic function of a random variable X.
Here are some examples of using the \varphi
command:
$$
\varphi_{\mathrm{Bin}(n,p)}(t) = (pe^{it} + 1 - p)^n
$$
$$ \varphi_{\mathrm{Bin}(n,p)}(t) = (pe^{it} + 1 - p)^n $$
This represents the characteristic function of a binomial distribution with parameters n and p.
$$
\varphi_{\mathcal{N}(\mu,\sigma^2)}(t) = e^{it\mu - \frac{1}{2}\sigma^2t^2}
$$
$$ \varphi_{\mathcal{N}(\mu,\sigma^2)}(t) = e^{it\mu - \frac{1}{2}\sigma^2t^2} $$
This represents the characteristic function of a normal distribution with mean $\mu$ and variance $\sigma^2$.
Remember that to use the \varphi
command in LaTeX, you need to include the package amsmath
in the preamble of your LaTeX document.
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