Provide an appropriate response.The standard normal probability density function is defined by f(x) = 
e- x2/2. (a) Show that 
dx = 
.(b) Use the result in part (a) to show that the standard normal probability density function has mean 0.
What will be an ideal response?
(a) 
dx = 
dx = 
= 
.
(b) Since y = 
x e- x2/2 is an odd function, 
dx = - 
dx = - 
. The mean of the distribution is equal to 
dx = 
dx + 
dx = - 
+ 
= 0.
You might also like to view...
Use the given transformation to evaluate the integral.
Rwhere R is the interior of the ellipsoid 
A. 
?
B. 
?
C. 
?
D. 42?
Find the domain and range of the inverse of the given function.f(x) = 
, x ? 0
A. Domain: (0, 2]; range: [0, ?) B. Domain: (-?, 0}; range: [-2, 0) C. Domain and range: [0, ?) D. Domain: [0, ?); range: (0, 2]
Find the median for the data given.Number of customers at concession stand: 35, 16, 5, 5, 27, 15, 28, 32, 40, 36
A. 24 customers B. 27 customers C. 28 customers D. 27.5 customers
The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.
A. y = 5 cos 
B. y = 5 cos (2x)
C. y = 5 sin 
D. y = 5 sin (2x)