Continuous Distributions (HSC SSCE Mathematics Advanced): Quizzes

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Continuous distributions
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For a continuous random variable XX, what is P(X=5)P(X = 5)?

00

For a CDF F(x)F(x) on interval [a,b][a, b], what is the value of F(b)F(b)?

11

How is the PDF f(x)f(x) related to the CDF F(x)F(x)?

f(x)=F′(x)f(x) = F'(x)

For f(x)f(x) to be a valid PDF on [a,b][a, b], what must ∫abf(x)dx\int_a^b f(x)dx equal?

11

Given CDF F(x)F(x), how do you find P(2≤X≤5)P(2 \leq X \leq 5)?

F(5)−F(2)F(5) - F(2)

For a uniform distribution on [a,b][a, b], what is f(x)f(x)?

1b−a\frac{1}{b-a}

To find the median using CDF F(x)F(x), solve for which equation?

F(x)=12F(x) = \frac{1}{2}

Which term refers to probability at a point?

Density

What is a mode of a PDF?

A global maximum

Why do [2,4][2, 4] and (2,4)(2, 4) have the same probability in continuous distributions?

P(X=h)=0P(X = h) = 0 for any value hh

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Sequences and Series

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The Trigonometric Functions

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Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

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Motion and Rates

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