Exactly, right?
But the definition says otherwise.
My point is: from the definition of probability density,
$$P_X(x) dx$$
is the probability that a random variable X has a value in [x,x+dx]. P(x) by itself is NOT the probability that the value of the random variable X will by precisely x...
Hello,
The following problem can be found in van Kampen's "Stochastic Processes in Physics and Chemistry", Third Edition (Exercise I.3.7):
The probability distribution of lifetimes in a population is P(t). Show that the conditional probability for individuals of age τ is...