Statistics and Probability (Final Exam)
random variable
is a function that associates a REAL NUMBER to each element in the SAMPLE space.
It is a variable determined by CHANCE
A random variable is a ________ random variable
if its set of possible outcomes is COUNTABLE.
Mostly, discrete random variables represent COUNT DATA, such as the number of
defective chairs produced in a factory.
A random variable is a __________ random variable
if it takes on values on a CONTINUOUS SCALE.
Often, continuous random variables represent MEASURED DATA, such as heights,
weights, and temperatures.
discrete probability distribution or probability mass function
consists of the values of random variable can assume and the CORRESPONDING
PROBABILITIES of the values.
Properties of a Probability Distribution
1. The probability of each value of the random variable MUST BE BETWEEN OR
EQUAL TO 0 to 1. In symbol, we write it as 0 ≤ P(X) ≤ 1.
2. The sum of the probabilities of all the values of the random variable MUST BE
EQUAL TO 1 symbol, we write it as ΣP(X) = 1.
μ = X₁ ⋅ P(X₁) + X₂ ⋅ P(X₂), X₃ ⋅ P(X₃) + . . . , + Xₙ ⋅ P(Xₙ)
or
μ = ΣX ⋅ P(X)
Formula for the Mean of the Probability Distribution
X₁, X₂, X₃, . . . , Xₙ
values of the random variable X
P(X₁), P(X₂), P(X₃), . . ., P(Xₙ)
corresponding probabilities
Steps in Finding the Variance and the Standard Deviation
1. Find the mean of the probability distribution.
2. Subtract the mean from each value of the random variable X.
3. Square the results obtained in Step 2.
4. Multiply the results obtained in Step 3 by the corresponding probability.
