Biostat Chapter 5 Flashcards
Probability
the proportion of times an event is expected to occur in the long run. Probabilities are always numbered between 0 and 1 with 0 corresponding to “never” and 1 corresponding to “always.”
random variable
a number that takes on different values
Population
the set of all possible outcomes for a random variable. (this refers to a hypothetical population of numbers, not a population of people.)
Event
an outcome, or set of outcomes, for a random variable
Discrete Random Variable
a countable set of possible outcomes
Continuous Random Variable
quantities that take on an unbroken continuum of possible values
PMF
Probability Mass Function
A mathematical relation that assigns probabilities to all possible outcomes for a discrete random variable
“A” denotes…
“event A”
Pr(A)
the probability of event A
_
A
denotes the complement of A (this means all events other than A; “not A”)
“S” represents…
The “sampling universe” or “sample space” of all possible outcomes.
4 Properties of functions
Property 1 (Range of Possible Probabilities): Individual properties are never less than 0 and never more than 1.
Formula: 0≤ Pr(A)≤1
Property 2 (Total probability): Probabilities in the sample space must sum to exactly 1.
Formula: Pr(S) =1
Property 3 (Compliments): The probability of a complement is equal to 1 minus the probability of the event.
Formula: _
Pr(A)= 1 - Pr(A)
Property 4 (Disjointed events): Events are disjointed if they cannot exist concurrently. If A and B are disjoint, then:
Formula: Pr(A or B)= Pr(A) + Pr(B)
Mean (μ) of PMF
μ = Σx · Pr(X=x)
often referred to as its value.
A weighted average of values with weights based on probabilities
Variance (σ^2) of PMF
σ2 = Σ(x-μ)^2 · Pr(X=x)
The weighted average of the squared distances around the mean with weights provided by probabilities
Area Under the Curve (AUC)
areas correspond to probabilities.
AUC= equal to the probability of the corresponding range in PMF and PDF graphs
