Russell & Norvig: Probability

Chapter 13: Quantifying Uncertainty

7 flashcards · Mathematics · by lakesare

1. Decision Theory is a combination of ___________ and __________?

   Decision Theory = Probability Theory + Utility Theory Consider again the A90 plan for getting to the airport. Suppose it gives us a 97% chance of catching our flight. Does this mean it is a rational choice? Not necessarily: there might be other plans, such as A180, with higher probabilities. If it is vital not to miss the flight, then it is worth risking the longer wait at the airport. What about A1440, a plan that involves leaving home 24 hours in advance? In most circumstances, this is not a…

2. Visually imagine the Central Limit Theorem.

   The central limit theorem states that the distribution formed by sampling n independent random variables and taking their mean tends to a normal distribution as n tends to infinity. This holds for almost any collection of random variables, even if they are not strictly independent, unless the variance of any finite subset of variables dominates the others

3. What does E(X) stand for?

   Expectation of a random variable X. The expected value of a random variable is denoted by E[X]. The expected value can be thought of as the "average" value attained by the random variable

4. How would you find the expectation of a random variable X?

   random variable output * its probability + random variable output * its probability +... random variable output * its probability. The expected value of a random variable is denoted by E[X]. The expected value can be thought of as the "average" value attained by the random variable

5. What's another name for: prior probability posterior probability.

   prior probability - unconditional probability prior = prior probability = unconditional probabilityposterior probability - conditional probability posterior = posterior probability = conditional probability

6. Give an example of a prior VS posterior.

   prior prior = prior probability = unconditional probabilityposterior posterior = posterior probability = conditional probability

7. What's the relationship between: the definition of the conditional P(a|b) The definition makes sense if you remember that observing b rules out all those possible worlds where b is false, leaving a set whose total probability is just P (b).the product rule P(a ∧ b) The product rule is perhaps easier to remember: it comes from the fact that, for a and b to be true, we need b to be true, and we also need a to be true given b.

   This is the same formula. For the definition of the conditional P(a|b) - imagine the circlesFor the product rule P(a ∧ b) - speak it out "probability of a and b = probability of b * probability of a given b"