Answer:
a) 
b) 
c)
![Var(X)=E(X^2)-[E(X)]^2= \frac{1}{2}(e^2 -1) -(e-1)^2 = 0.242](https://tex.z-dn.net/?f=Var%28X%29%3DE%28X%5E2%29-%5BE%28X%29%5D%5E2%3D%20%5Cfrac%7B1%7D%7B2%7D%28e%5E2%20-1%29%20-%28e-1%29%5E2%20%3D%200.242)
Step-by-step explanation:
a) what must the value of C be so that f(x) is a probability density function?
In order to be a probability function we need this condition:

And solving the left part of the integral we have:

, so then 
b) find P(X<2)
We can find this probability on this way using the density function:

c) find E(X) and Var(X)
We can find the expected value on this way:
In order to find the Var(X) we need to find the second moment given by:
And now we can use the following definition:
![Var(X)=E(X^2)-[E(X)]^2= \frac{1}{2}(e^2 -1) -(e-1)^2 = 0.242](https://tex.z-dn.net/?f=Var%28X%29%3DE%28X%5E2%29-%5BE%28X%29%5D%5E2%3D%20%5Cfrac%7B1%7D%7B2%7D%28e%5E2%20-1%29%20-%28e-1%29%5E2%20%3D%200.242)
Answer:
=5
Step-by-step explanation:
4-9= -5
2-3 = -1
=5
.....
Answer: c= 14 * t
Explanation:
The first day:
280/20= 14
Second day:
490/35= 14
That is how it does not change from day to day, the average is 14 calories per minute,therefore, the equation would be:
c= 14 * t
Answer: 10
Step-by-step explanation: volume of rectangular prism=length x height x width
volume of rectangular prism=8 x5x1/4
Volume of rectangular prism =10