Chpt 5 - Discrete Random Variables Flashcards
What is a random variable?
A variable whose possible values are:
-Numerical
-Depend on chance
What are the 2 types of random variables?
Discrete random variable
Continuous random variable
What is a variable whose possible values are numerical and are depending on chance?
Random variable
What is a discrete random variable?
A random variable whose possible values can be listed
(I understand this as whole numbers)
How do we show the distribution of a random variable?
We can use a graph, table, or formula to show:
-possible values
-relative frequency
(so what and how often)
What do we use to denote a random variable and the values that it can take
X - random variable
x - possible values the variable can take
What does P(X = 1) mean?
The probability of the variable being equal to 1
So 1 email address, 1 child at home, has 1 pet etc.
What does P(X < 2) mean?
The probability of the variable being less than 2
So 1 or no kids at home, maybe 1 or no pets for example
What is the value of:
P(X = x)
0 - 1
Because it is a probability
How do we denote the probability of a value of a random variable?
P(X = x)
P is probability
X is the random variable
x is the value the variable can take that we are looking at
What is the sum of all the probabilities of a random variable?
1
Each individual value will be between 0-1 as it is probabilities of the entire population. The entire population counted together is 1 (meaning its 100%)
Distribution of a value is:
x -1 0 1
X 0.5 0.3 0.4
Is this distribution correct? Why/why not?
No, because the sum is greater than 1
You have a distribution table as follows:
x 0 1 2
X 0.4 0.2 a
What should the value of a be?
a = 1 - 0.4 - 0.2 = 0.4
How do we describe the center when discuss the distribution of a discrete random variable?
Population means - but only if we have the population data available, if not, we use relative frequencies
What is the formula for determining the population mean of a discrete random variable X?
μ = ∑ xP(X=x)
So we multiply each value (x) by it’s own probability (P(X=x)) and then add up all of these to create the average, or mean (mu)
What are the steps to determining the population mean of a discrete random variable?
μ = ∑ xP(X=x)
- Multiply each possible value (x) and it’s corresponding probability ( P(X=x) )
- Add all the values in 1 up to determine the mean