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Chapter 5

# Stats 2035 Chapter 5 Notes

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Western University

Statistical Sciences

Statistical Sciences 2035

Histro Sendov

Fall

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Chapter 5: Continuous Random Variables
Continuous Probability Distributions
Continuous random variable: May assume any numerical value in one or more intervals
Continuous probability distribution: Assigns probabilities of intervals of values
o Many businesses measures such as sales, investments, costs, and revenues can be represented by continuous
random variables
o Other names for a continuous probability distribution: probability curve, probability density function
o The function f(x) is the continuous probability distribution of random variable X if P(a <= X <= b) = the area
under the graph of f(x) between a and b.
o Properties of f(x):
f(x) >= 0 for all x
The total area under the curve of f(x) is equal to 1
P(X = a) = P(X = b) since they are of a line is 0. So, P(a <= X <= b) = P(a < X < b)
Let x be the continuous probability distribution of random variable x
o The points where f is non-zero are the possible values of the random variable X
o P(a <= X <= b) = The area under the graph of f(x) between a and b
o The proportion of population that is in [a,b]
o Why is P(X = a) = 0? How can the proportion of the population that is equal to a be 0?
A population that has cont

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