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Random variables (A random variable assigns a unique numerical value to…
Random variables
A
random variable
assigns a unique numerical value to the outcome of a random experiment
Theoretical
Apply principles of probability
Observational
Use relative frequency
Discrete random variable
Count
Continuous random variable
Measure
Discrete random variables
P(X = x)
denotes the probability that the discrete random variable gets the value x
Probability distribution
All the possible values of a discrete random variable, along with their associated probabilities
The probability distribution of the random variable X is easily summarized in a table
and
Mean and Variance
Mean
(sometimes referred as
expected value
)
Variance
Standard deviation
Rules for a + bX (Linear Transformation of One Random Variable)
Rules for X + Y (Sum of Two Random Variable):
(If the random variables are independent)
Binomial Random Variables
Binomial experiment
A fixed number (n) of trials
Each trial must be independent of the others
Each trial has just two possible outcomes, called "
success
" (the outcome of interest) and "
failure
"
There is a constant
probability (p) of success
for each trial, the complement of which is the
probability (1 - p) of failure
Rule of Thumb
The number (X) of successes in a sample of size n taken without replacement from a population with proportion (p) of successes is approximately binomial with n and p as long as the sample size (n) is at most 10% of the population size (N):
Mean and Standard deviation
Continuous Random Variables
Probability Distribution
Probability density curve
Normal Random Variables
Z-score
Standard normal table
Normal Approximation to the Binomial
np >= 10 and n(p - 1) >= 10
Continuity correction
