Frequentist calculation

Front

What is the definition of Frequentist probability?

Back

Frequentist probability is defined as the limit of the relative frequency of an event occurring after many trials. It is based on the idea that probabilities can be estimated by observing the outcomes of repeated experiments.

Front

What does θ represent in the context of coin flipping?

Back

In the context of coin flipping, θ represents the probability of getting heads (H) when the coin is flipped.

Front

How do you calculate the probability of a sequence of coin flips?

Back

The probability of a sequence of coin flips is calculated by multiplying the probabilities of each individual flip. For example, p(HTH) = p(H) * p(T) * p(H).

Front

What is the formula for finding the maximum likelihood estimate (MLE) of θ?

Back

The MLE of θ is found by maximizing the likelihood function, which is the probability of observing the data given θ. This often involves taking the derivative of the likelihood function and setting it to zero.

Front

What is the likelihood function for observing the sequence HTH?

Back

The likelihood function for observing the sequence HTH is L(θ) = θ^2 * (1-θ), where θ is the probability of heads.

Front

What is the significance of the derivative ∂p(HTH) / ∂θ = 0?

Back

Setting the derivative ∂p(HTH) / ∂θ = 0 helps to find the value of θ that maximizes the likelihood of observing the data, which is the maximum likelihood estimate.

Front

If θ = 2/3, what is the probability of observing HTH?

Back

If θ = 2/3, the probability P(HTH | θ=2/3) is calculated as (2/3) * (1/3) * (2/3) = 4/27.

Front

What is the relationship between the number of trials and the accuracy of Frequentist probability?

Back

As the number of trials increases, the accuracy of the Frequentist probability estimate improves, converging towards the true probability.

Front

What is a common misconception about Frequentist probability?

Back

A common misconception is that Frequentist probability can provide the probability of a single event occurring, when in fact it is based on long-term frequencies.

Front

What is the difference between Frequentist and Bayesian probability?

Back

Frequentist probability relies on long-run frequencies and does not incorporate prior beliefs, while Bayesian probability incorporates prior beliefs and updates them with new evidence.