Transcript Probability Distributions - University of Southampton

Probability Distributions
Some of the more general
probability distributions.
Probability Distributions
• Graphs – the horizontal axis represents the
range of values a variable can take and the
vertical axis represents the probability of the
event.
Unimodal Distribution
• This graph is an example of a unimodal
distribution as it has only one peak.
Bimodal Distribution
• This graph is an example of a bimodal
distribution as it has two peaks. Notice that they
do not have to be the same height.
Skewed Distribution
• A skewed distribution has its peak off to one side
(not in the middle).
Symmetric Distribution
• Symmetric distributions are as the name
suggests, symmetric about the central vertical
line.
Mean
• In a symmetric graph, like the one on the left, the
mean value will be at the peak.
• In a skewed graph, like the one on the right, the
mean value will not be at the peak. In this
example it will be to the left of the peak.
Large standard deviation
• This graph has a large standard deviation as it’s
peak is wide and short.
Small standard deviation
• This graph has a small standard deviation as it’s
peak it tall and narrow.
Area under the curve
• The area under the curve indicates what the
probability of that outcome is, so for example in
this graph it is very likely (about 80%) for an
event to occur in the range between the two
small vertical lines.
Area under the curve
• In this graph it is quite unlikely (about 10%) for
an event to occur at a value less than the small
vertical line.
Area under the curve
• In this graph it is highly likely (about 90%) for an
event to occur at a value greater than the small
vertical line.