False.

The argument of a likelihood function is not the potential value of the observed data. Instead, it is the parameter(s) of the statistical model given the observed data. The likelihood function describes how probable the observed data is for different values of these parameters.

To elaborate, given data $X$ and a statistical model parameterized by $\theta$:

• Probability Function: $P(X \mid \theta)$ is the probability of observing the data $X$, given a parameter value $\theta$.
• Likelihood Function: $L(\theta \mid X)$ is the likelihood of the parameter value $\theta$ given the observed data $X$.

The likelihood function $L(\theta)$ uses the observed data to express the probability as a function of the parameters.

Would you like further details or have any questions?

Relative Questions:

1. What is the difference between a likelihood function and a probability density function?
2. How is the maximum likelihood estimate (MLE) determined using the likelihood function?
3. Why is the likelihood function maximized instead of minimized when estimating parameters?
4. What role does the log-likelihood play in statistical analysis?
5. Can you explain an example of how a likelihood function is applied in real-world statistics?

Tip: In many cases, it is easier to maximize the log-likelihood rather than the likelihood itself, as taking the natural logarithm simplifies multiplication into addition.