For each probability density function, over the given interval, find E ( x ) , E ( x 2 ) , the mean, the variance, and the standard deviation. f ( x ) = 1 ln 5 ⋅ 1 x , [ 1.5 , 7.5 ]
For each probability density function, over the given interval, find E ( x ) , E ( x 2 ) , the mean, the variance, and the standard deviation. f ( x ) = 1 ln 5 ⋅ 1 x , [ 1.5 , 7.5 ]
Solution Summary: The author calculates the value of E(x) and the variance and standard deviation for the provided probability density function.
Let
f(x) = k(3x − x2)
if
0 ≤ x ≤ 3
and
f(x) = 0
if
x < 0
or
x > 3.
(a)
For what value of k is f a probability density function?
k =
(b)
For that value of k, find
P(X > 1).
P(X > 1) =
(c)
Find the mean.
? =
Consider the function given below:f(x) = kx2 0 < x < 2.13What must be the value k so that f(x) is a valid probability density function?
et
f(x) = k(9x − x2)
if
0 ≤ x ≤ 9
and
f(x) = 0
if
x < 0
or
x > 9.
(a) For what value of k is f a probability density function?
k =
6729
(b) For that value of k, find
P(X > 1).
P(X > 1) =
(c) Find the mean. ? =
Precalculus Enhanced with Graphing Utilities (7th Edition)
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