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

The correct answer is B. 1 and 2.

The exponential distribution is a continuous probability distribution that is often used to model the time between events. It has one parameter, $\lambda$, which is the rate of the event. The Gaussian distribution, also known as the normal distribution, is a continuous probability distribution that is often used to model the distribution of data. It has two parameters, $\mu$ and $\sigma^2$, which are the mean and variance of the data.

The number of parameters in a probability distribution is the number of quantities that need to be specified in order to completely determine the distribution. For example, the exponential distribution is completely determined by the value of $\lambda$, so it has one parameter. The Gaussian distribution is completely determined by the values of $\mu$ and $\sigma^2$, so it has two parameters.

Here is a brief explanation of each option:

• Option A: 2 and 2. This is incorrect because the exponential distribution has one parameter and the Gaussian distribution has two parameters.
• Option B: 1 and 2. This is the correct answer because the exponential distribution has one parameter and the Gaussian distribution has two parameters.
• Option C: 2 and 1. This is incorrect because the exponential distribution has one parameter and the Gaussian distribution has two parameters.
• Option D: 1 and 1. This is incorrect because the exponential distribution has one parameter and the Gaussian distribution has two parameters.