Question

The number of parameters in the univariate exponential and Gaussian distributions, respectively are

• A. 2 and 2
• B. 1 and 2
• C. 2 and 1
• D. 1 and 1

Answer 1

The correct option is B 1 and 2

Probability distribution function (PDF) of an exponential distribution is

$f(x,\lambda )=(\begin{array}{cc}{\mathrm{\lambda e}}^{-\mathrm{\lambda x}}& x\ge 0\\ 0& x<0\end{array}$

Cumulative distribution function of an exponential distribution is

$f(x,\lambda )=(\begin{array}{cc}1-e^{-\mathrm{\lambda x}}& x\ge 0\\ 0& x<0\end{array}$

where $\lambda >0$ is the parameter of distribution. So only one parameter in exponential distribution.

The normal (or Gaussion) distribution is a very common continuous probability distribution.

The probabbility density of normal distribution is

$f\left(x\right)=\frac{1}{\sqrt{2\pi {\sigma }^2}}{e}^{-\frac{(x-\mu {)}^2}{2{\sigma }^2}}$

So there are two parameters i.e. $\left(\mu \text{and}{\sigma }^2\right)$ in gaussian distribution.