PDF and CDF
Understand relation between Probability Density Function (PDF) and Cumulative Distribution Function (CDF).
If X is continuous, the probability density function, f, is defined such that:
\[( P( a\leq X \leq b) = \int_a^b f(x) dx\]
The cumulative distribution function, F, of a discrete random variable X that has a probability distribution described by P(x\(_i\)) is defined as: \[F(x_m) = \Sigma P(x_k) = P(X \leq x_m), m = 1,2,...,n\]
If X is continuous, the cumulative distribution function, F, between a and b, is defined by:
\[\int_a^b f(x) dx\]
Let X denotes the time a person waits for a bus to arrive as shown below. Calculate the probability that a person waits 90 seconds for the bus to arrive.