Transcript Clicker Question 1

Clicker Question 1
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What, in radical form, is the Simpson’s Rule
estimate (with n = 2) of the surface area
generated by rotating y = x about the xaxis between x = 0 and x = 2?
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A. (1 + 3 + 5 + 7 + 9)
B. (1 + 43 + 25 + 47 + 9)
C. /3 (1 + 43 + 25 + 47 + 9)
D. /6 (1 + 43 + 25 + 47 + 9)
E. /6 (1 + 23 + 45 + 27 + 9)
Probability (10/7/13)
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A continuous random variable X represents all
the values some physical quantity can take (e.g.,
heights of adult males, lifetime of a type of light
bulb, etc., etc.)
A probability density function f for X is a
function whose integral from a to b gives the
probability that X lies between a and b.
A density function must be non-negative and must
satisfy that its improper integral from - to  is 1.
Example
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Show that f (x) = 0.006x(10 – x) on [0, 10]
and 0 elsewhere is a density function.
If X is a random variable whose density
function is f , what is the probability X has a
value between 1 and 5?
Clicker Question 2
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Using the density function on the previous
slide, what is the probability that X is greater
than 3?
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A. 0.667
B. 0.784
C. 0.284
D. 0.845
E. 0.392
Mean Value of a Random Variable
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We can compute the mean, or average, value of a
random variable by adding up each of its values
weighted by the probability of that value, i.e.
compute 
 xf ( x)dx

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In our example, what is the mean value of the
variable (obvious from the symmetry of f, but work it
out)?
Question: What, in general, would the median be?
The Normal Density Function
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The “mother of all density functions” is the normal
density function
2
2
1
 2
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e ( x   )
/( 2 )
where  is the mean and  is the standard
deviation.
Note that we cannot use the Fundamental
Theorem to calculate probabilities with the function.
Hence we must use numerical methods instead.
Assignment for Wednesday
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Read Section 8.5.
In that section, please do Exercises 1, 4, 5,
and 9.
Wednesday’s class will have no clicker
questions. We will go over this last material
and then review as needed.
Test #1 is on Friday. You can start at 8:30 if
you wish. One reference sheet can be used.