Provide an appropriate response.The standard normal probability density function is defined by f(x) = 
e- x2/2. (a) Use the fact that 
dx = 1 to show that 
dx =
.(b) Use the result in part (a) to show that the standard normal probability density function has variance 1.
What will be an ideal response?
(a) Since 
dx = 1 and f(x) is an even function, 
dx = 
. Then 
dx = 
dx = 
= 
dx = 
.
(b) The variance of the distribution is equal to 
dx = 
dx + 
dx = 
+ 
= 1.
You might also like to view...
Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines.
,
y = 4,
x = 2; revolve about the line 
A. 
?
B. 
?
C. 
?
D. 
?
Find the least common multiple of the given number by the method of intersection of sets of multiples.84 and 126
A. 504 B. 252 C. 42 D. 756
Provide an appropriate response. A business paid a $6.32 finance charge on a monthly balance of $412.52. What was the monthly rate of interest? Round to the nearest hundredth.
A. 6.5% B. 1.53% C. 18.36% D. 1.63%
Evaluate the function requested. Write your answer as a fraction in lowest terms.
Find cos B.
A. cos B = 
B. cos B = 
C. cos B = 
D. cos B = 