Answer:
(a) moment generating function for X is 
(b) 
Step-by step explanation:
Given X represents the number on die.
The possible outcomes of X are 1, 2, 3, 4, 5, 6.
For a fair die, 
(a) Moment generating function can be written as
.



(b) Now, find
using moment generating function




Hence, (a) moment generating function for X is
.
(b) 
Answer:

Step-by-step explanation:
The Given question is INCOMPLETE as the statements are not provided.
Now, let us try and solve the given expression here:
The given expression is: 
Now, the BINOMIAL EXPANSION is the expansion which describes the algebraic expansion of powers of a binomial.
Here, 
or, on simplification, the terms of the expansion are:

The above statement holds for each n > 0
Hence, the complete expansion for the given expression is given as above.
The equivalent expression to the given one is -sin(pi/6).
<h3>
</h3><h3>
Which expression is equivalent to the given one?</h3>
The given expression is:
sin(7pi/6)
Where the argument is in radians.
Remember that:
sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)
Now we can rewrite:
sin(7pi/6) = sin(pi + pi/6)
Then we can use the above relation to rewrite:
sin(pi + pi/6) = sin(pi)*cos( pi/6) + sin(pi/6)*cos(pi)
And we know that:
sin(pi) = 0
cos(pi) = -1
Then we can write:
sin(7pi/6) = - sin(pi/6)
If you want to learn more about the sine function:
brainly.com/question/9565966
#SPJ4
Answer:
It's B.
Step-by-step explanation:
Answer:
Please see the attachment for double number line.
Explanation:
We are given cost of 4 water bottles is $10
We can write ,
Cost of 4 bottles = $10
Cost of 1 bottle = $2.5
Cost of 2 bottles =$5
Cost of 3 bottles =
= $7.5
Cost of n bottles = $2.5n
Now we draw the double number line.
Bottom line(Line 1) will take as number of bottles:
1 2 3 4 5 6
Above line (Line 2) will show the cost of corresponding number of bottles:
2.5 5 7.5 10 12.5 15