Math Problem Statement
Suppose the density function for a random variable X is given by f(x) .
It is known that the density function f(x) > 0 between -31.7 and 14 . Outside of that range, f(x) equals zero.
( Translation, the density curve is above the x-axis between the numbers -31.7 and 14. Otherwise, the density curve is the x-axis )
Determine F( 14 ) = P( X<= 14 )
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Probability Density Function
Cumulative Distribution Function
Formulas
F(x) = P(X ≤ x) = ∫ f(t) dt from -∞ to x
F(14) = ∫ f(x) dx from -31.7 to 14
Theorems
Fundamental Theorem of Calculus
Properties of Probability Distributions
Suitable Grade Level
Grades 11-12 and College-level Probability
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