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Flashcards
What is a random variable??
A variable whose value depends on the outcome of a random event.
What is the notation for a random variable??
Capital letters, $X$.
What is the notation for the random variable $X$ taking a particular value $x$??
$$ P(X = x) $$
Can you explain $P(X = x)
The probability that the outcome of the random variable $X$ was the specific outcome $x$.
What’s the shorthand for $P(X = heads)$??
$$ p(heads) $$
What is a discrete uniform distribution??
A distribution that can only take specific values, which all have the same probability for each outcome.
What is a piecewise function??
We choose the function from a list depending on the input.
What is $P(X = 2)$??
$$ 0.2 $$
What is $P(X = 3)$??
$$ 0.3 $$
What is the advantage of writing probability distributions as a function??
You can have a rule or expression based on the outcome.
What is the advantageo f writing probability distributions as a table??
It’s easier to see the probability for each outcome.
What is the underlying sample space for $X$, the number of heads when three coins are tossed??
$$ HHH, HHT, HTT, HTH, THH, THT, TTH, TTT $$
What was the head of the table be for the probability distribution of $X$, the number of heads when three coins are tossed??
Number of heads, $x$.
In a probability distribution table where all possible outcomes are listed, what must the sum of all probabilities equal??
$$ 1 $$
What would that notation for “the sum of all probabilities”??
$$ \sum p(x) $$
What is $P(X > 3)$??
$$ 0.6 $$
For a discrete random variable, what is $p(x)$ called??
The probability mass function.
Why is $p(x)$ called a probability mass function for a discrete random variable??
Because the probability of each outcome represents an actual amount of the overall probability.
Visualise what the graphical probability distribution would look like for a six-sided die??
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Metadata
date: 2021-01-26 09:00
tags:
- '@?stats'
- '@?probability'
- '@?distributions'
- '@?year-1'
- '@?public'
- '@?school'
title: Stats - Statistical Distributions
