PROBABILITY. CONDITIONAL PROBABILITY Random variable A variable defined on a sample space. Fx: The...

PROBABILITY

CONDITIONAL PROBABILITY

Random variable• A variable defined on a sample space. Fx: The value of a card.•Interpretation: A variable that takes different values with different probabilities.

(Some) Characteristics of a random variable X: •Mean value E(X).•Variation V(X) = E((X-E(x))^2).

Graphical representation by histogram.

Cumulative mass function/distribution function of a random variable:F(x) = P(X ≤ x)

BINOMIAL DISTRIBUTION

BINOMIAL DISTRIBUTION

BINOMIAL DISTRIBUTION

POISSON DISTRIBUTION

POISSON DISTRIBUTION

POISSON DISTRIBUTION

CONTINOUS DISTRIBUTIONS

CONTINOUS DISTRIBUTIONS

NORMAL DISTRIBUTION

NORMAL DISTRIBUTION

NORMAL DISTRIBUTION

NORMAL DISTRIBUTION

LOG-NORMAL DISTRIBUTION

Fractile/QQ-plotsHow can we access information about the distribution of a sample?By comparing fractiles – the QQ-plot in SPSS.

The proposed distribution is good, if the fractiles follow a linear pattern.

Notice:•The variability of the points decreases when the sample size increases.•The variation of the points around the line is largest in the ends. Hence, pay more attention to the points in the middle of the plot.

Detrended QQ-plots•The points should be spread evenly above/below the horizontal line.•There should be no pattern.

Examples of QQ-plots

Normal distribution Skew distribution Uniform distribution

QQ-plot QQ-plotQQ-plot

Detrended QQ-plot Detrended QQ-plotDetrended QQ-plot