Textbook Notes (362,734)
Chapter 5

# Stats 2035 Chapter 5 Notes

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School
Western University
Department
Statistical Sciences
Course
Statistical Sciences 2035
Professor
Histro Sendov
Semester
Fall

Description
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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