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Probability theory and statistics
Chapter 2
Random variables
Random variable
Random variable and probabilities
Problem: Events defined by a random variable
Distribution functions
CDF, cumulative distribution function
Discrete random variable and probability mass function
Discrete random variable: probability mass function versus cumulative distribution function
Continuous random variable and the probability density function
The pdf and the cdf of a continuous random variable
The standard normal random variable
Standard normal
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Problem: Events defined by a random variable
Problem
True or false?
\(\{ X<a \}⊆\{ X<b \}\)
if
\(a<b\)
.
\(P\left( X<a \right)≤P\left( X<b \right)\)
if
\(a<b\)