letcture 4

Question 1

Probability primer - random variables

Answer 1

A random variable is the basic element of probability

refers to an event and there is some degree of uncertainty as to the outcome of the event.

for example, the random variable A could be the event of getting a heads on a coin flip

Question 2

boolean random variables

Answer 2

take the values true or false

think of the event as occurring or not occuring

Question 3

probabilty

Answer 3

the relative frequency with whih an outcome would be obtained of the process were repeated a large number of times under similar conditions.

Question 4

Joint probability distribution

Answer 4

joint probabilities can be between any number of variables.

for each combination of variables, we need to say how probable that combination is

the probabilities of these combinations need to sum to 1.

Question 5

Independence

Answer 5

The outcome of the 2nd throw is independent of the outcome of the 1st one.

whwether it will rain in Nijmegen tomorrow is independent of today’s stock trading price of KLM.

how is it useful?
*suppose you have n coin filips and you want to calculate the joint distrubuition P(c1,….Cn)

• if the coin flips are not independent, you need to specify s^n -1 values in the table
• if the coin flips are independent, then

P(C1…..Cn) = sum of P(C1)

Question 6

learning goals: reasoning with uncertainty

Answer 6

working with basic probabilistic concepts such as ( conditional) independence.

*applying Bayes rule to compute the probability of cause given effect for a example involving just a few variables.

exlaaining basic structures such as a casual chain, a common cause , and a common effect.