Probability Distributions
Since the value of a random variable cannot be predicted accurately, by convention, probabilities are assigned to all the likely values that the variable may take. For example, if the price of a share of Dowell Limited could have possible values of Rs.15, Rs.20, Rs.23, Rs.25 and Rs.30, the chances of the actual price taking on any of these values may be described by attaching probabilities of 0.12, 0.20, 0.08, 0.10 and 0.50 respectively to the prices. By enumerating the possible values and assigning probabilities specifically to each of these values, we are in fact, describing a probability distribution of share prices.
X
P(X)
15
20
23
25
30
0.12
0.20
0.08
0.10
0.50
With the help of the above probability distribution, it can be inferred that there is a 50% chance for the price to touch Rs.30 and there is only an 8% chance for the price to assume a value of Rs.23. The probability distribution can give an idea of the likely values of a random variable and the chances of occurrence of the various values.