Review of Probability Concepts ECON 4550 Econometrics Memorial University of Newfoundland Adapted from Vera Tabakova’s notes
B.1 Random Variables B.2 Probability Distributions B.3 Joint, Marginal and Conditional Probability Distributions B.4 Properties of Probability Distributions B.5 Some Important Probability Distributions
A random variable is a variable whose value is unknown until it is observed. A discrete random variable can take only a limited, or countable, number of values. A continuous random variable can take any value on an interval.
The probability of an event is its “limiting relative frequency,” or the proportion of time it occurs in the long-run. The probability density function (pdf) for a discrete random variable indicates the probability of each possible value occurring.
Figure B.1 College Employment Probabilities
The cumulative distribution function (cdf) is an alternative way to represent probabilities. The cdf of the random variable X, denoted F(x), gives the probability that X is less than or equal to a specific value x
For example, a binomial random variable X is the number of successes in n independent trials of identical experiments with probability of success p.
For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks
First: for winning only once in three weeks, likelihood is 0.189, see? Times
For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks… The likelihood of winning exactly 2 games, no more or less:
For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks So 3 times = is the likelihood of winning exactly 2 games
For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks And is the likelihood of winning exactly 3 games
For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks For winning only once in three weeks: likelihood is is the likelihood of winning exactly 2 games is the likelihood of winning exactly 3 games So is how likely they are to win at least 2 games in the next 3 weeks In STATA di Binomial(3,2,0.7) di Binomial(n,k,p)
For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks So is how likely they are to win at least 2 games in the next 3 weeks In STATA di binomial(3,2,0.7) di Binomial(n,k,p) is the likelihood of winning 1 or less (See help binomial() and more generally help scalar and the click on define) So we were looking for 1- binomial(3,2,0.7)
For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks So is how likely they are to win at least 2 games in the next 3 weeks In SHAZAM, although there are similar commands, but it is a bit more cumbersome See for example:
For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks Try instead: rnoulli.html rnoulli.html GRETL: Tools/p-value finder/binomial
Figure B.2 PDF of a continuous random variable If we have a continuous variable instead
y 0.04/.18= /.18=.78
Two random variables are statistically independent if the conditional probability that Y = y given that X = x, is the same as the unconditional probability that Y = y.
Y = 1 if shaded Y = 0 if clear X = numerical value (1, 2, 3, or 4)