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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Find the probability that x lies in the interval 1 2 x 1 for the probability density function in Checkpoint 1.

To determine

To calculate: The probability that x lies in the given internal for the given probability density

function f(x)=12x.

Explanation

Given Information:

The probability density function f(x)=12x and interval 12x1 .

Formula used:

Let f be a function of a continuous random variable x whose set of interval is [a,b].

Then the probability that x lies in the interval [c,d] is,

P(cxd)=cdf(x)dx

The anti-derivative (integral) of a polynomial function can be written as,

xnadx=1a×xn+1n+1+c3

Where n1 and c3=constantanda=someconstant.

According to the fundamental theorem of calculus, if f(x) is a function that is continuous in

[a,d] and f(x) is the anti-derivative of the function,

Then,

abf(x)dx=f(x)|ab=f(b)f(a)

Calculation:

Consider the function given,

f(x)=12x

From the primary equation, the probability that x lies in 12x

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