Characteristics of Probability Distributions

The probability distribution shows the maximum range that a particular random variable can have and their corresponding probability value.

• The curve is bell shaped curve
• It is symmetrical about the mean µ.the mean divides the distribution into two equal parts, one to the left of the mean whereas the other to the right of it. One part is a mirror image of the other.The skewness is zero in this distribution.
• There is a coincidence between the mean, median and mode.
• The distribution is a continuous normal distribution.
• The range of possibility out come is infinite. This can be implied from the very fact that the curve is bell shaped. The limit extends to negative infinity at one end and positive infinity at the other end.
• Most of the outcome is usually clustered in and around the middle, which can also be termed as the mean of the distribution.
• The closeness of the clusters is defined by their standard deviation.
• The complete distribution can be described completely with the help of mean and the standard deviation of the distribution.
• In this distribution the value of mean is equivalent to median which in turn is equal to mode. This mean the value of mean, median and mode are equal.
• The mean and standard deviation varies with the value of the random variable. These are the two factors that define the shape of the probability distribution curve.
• There are two type of distribution based on the no of variable whose probability can be determined using the curve. The two types are uni variable distribution and multi variable distribution. In case of uni variable distribution it explains the probability distribution of a single variable, whereas in case of multi variable it describes the probability distribution of more than one variable. In case of multi variable it combines the distribution of more than one random variable. In case of uni variable distribution the complete distribution is described with the help of mean and standard deviation, whereas it is not true in case of multi variable distribution. In case of multivariable a third factor is needed and that is correlation.