The integral of the derivative of F(x) from negative infinity to positive infinity is1;

b= 1，a=- 1 .

For example:

p( 1 & lt； X & lt2)

=∫( 1->； 2) ( 1/2)e^(-x) dx

=-( 1/2)[e^(-x]]( 1->； 2)

=( 1/2)[e^(- 1]-e^(-2]

Extended data:

Although P{X=a}=0, {X=a} is not an impossible event. Similarly, the probability of an event is 1, which does not mean that this event must be an inevitable event. When referring to the probability distribution of random variable X, it refers to its distribution function, the probability density when X is continuous, and the distribution law when X is discrete.

Random variables that can be listed one by one in a certain order and whose range is one or several finite or infinite intervals are called discrete random variables. Discrete random variables and continuous random variables are also determined by the range (or form) of random variables, and variables can only take discrete natural numbers, that is, discrete random variables.

Baidu Encyclopedia-Continuous Random Variable