Introduction to Probability
Definition 1.0.1. An experiment is a procedure we perform (quite often hypothetical) that
produces some result.
Definition 1.0.2. An outcome is a possible result of an experiment.
Definition 1.0.3. An event is a certa
The most important theoretical results in probability theory are limit theorems. Of these, the
most important are Laws of large numbers and Central limit theorems.
Definition 5.0.119 (Markovs inequality). If X is a random variable
1. Find the area under the standard normal curve between (a) z = -1.20 and z =2.40, (b) z =1.23
and z =1.87, (c) z = -2.35 and z = -0.50.
2. If Z is normally distributed with mean 0 and variance 1, find: (a) P(Z -1.64), (b) P(-1.96 Z
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Continuous Random Variable
Definition 3.0.74. X is a continuous random variable if there exists a nonnegative function
f , defined for all real x R, having the property that, for any set B of real numbers,
P(X B) =
The function f is