Answer:
a) Mean, E(X) = - 0.5
Variance = = 9.25
b) 
or
⇒ 
⇒ 
Step-by-step explanation:
Given:
moment generating function of X as:
MX(t) = 
a) Now
Mean, E(X) =
Thus,

or

also,
Thus,

or

Therefore,
Mean, E(X) = 
or
Mean, E(X) = - 0.5
and

or
= 9.5
also,
Variance(X) = E(X²) - E(X)²
⇒ 9.5 - (-0.5)²
= 9.25
b) Now,
Let f(x) be the PMF of X
Thus,

or
⇒ 
⇒ 
Therefore,
at x = 0, P(x) =
at x= - 4 ,P(x) = 
at x = 5, P(x) =
Thus,
E(X) =
or
E(X) = - 0.5
also,
= 9.5
Hence,
Var(X) = E(X²) - E(X)²
⇒ 9.5 - (-0.5)²
= 9.25
Answer:
the answer is 6 and below
Answer:
14 cm squared
Step-by-step explanation:
The shaded triangle is clearly half of the rectangle, and half of 28 is 14.
The other way you can look at it is that the dimensions of the rectangle are 4 cm and 7 cm. The area of a triangle equation is
. So
is 14.
Answer:
800 miles
Step-by-step explanation:
Set up an equation, where x is the number of miles driven:
0.10x + 120 = 200
Then, solve for x:
0.10x = 80
x = 800
So, the maximum number of miles he can drive is 800 miles
Answer: 8.5π
<u>Step-by-step explanation:</u>
If I understand the question correctly, the entire circle has an Area of 9π and you are looking for the Area of the shaded region which has a central angle of 
the section of the circle that is shaded is 
Area of the shaded region is: 