Why do we multiply two independent events?

Why do we multiply two independent events?

The multiplication rule for independent events relates the probabilities of two events to the probability that they both occur. In order to use the rule, we need to have the probabilities of each of the independent events.

Is likelihood function the same as PDF?

Therefore, the likelihood function is not a pdf because its integral with respect to the parameter does not necessarily equal 1 (and may not be integrable at all, actually, as pointed out by another comment from @whuber).

What does the U stand for in probability?

U(a,b) uniform distribution. equal probability in range a,b.

How to calculate the likelihood of a distribution?

In the likelihood we suppose that there is a sample x 1, x 2, …, x n of n independent and identically distributed observations (iid), coming from a distribution with an unknown probability density function , that means this joint density function is f ( x 1, x 2,…, x n | θ) = ∏ i = 1 i = n f ( x i | θ).

Why do we multiply the probabilties of ocurrence?

In short, the probabilty that you arrived at the sample that you have at hand. The goal of the maximum likelihood method is find estimator that maximize the probability of observe certains values of the variable ( endogenous variable). That is the reason why we must multiply the probabilties of ocurrence.

Is the log likelihood the same as the total probability?

The log likelihood. The above expression for the total probability is actually quite a pain to differentiate, so it is almost always simplified by taking the natural logarithm of the expression. This is absolutely fine because the natural logarithm is a monotonically increasing function.

Why are probability density and maximum likelihood different?

But despite these two things being equal, the likelihood and the probability density are fundamentally asking different questions — one is asking about the data and the other is asking about the parameter values. This is why the method is called maximum likelihood and not maximum probability.