Answer:
(a): Marginal pmf of x


(b): Marginal pmf of y


(c): Mean and Variance of x


(d): Mean and Variance of y


(e): The covariance and the coefficient of correlation

Step-by-step explanation:
Given
<em>x = bottles</em>
<em>y = carton</em>
<em>See attachment for complete question</em>
<em />
Solving (a): Marginal pmf of x
This is calculated as:

So:






Solving (b): Marginal pmf of y
This is calculated as:

So:






Solving (c): Mean and Variance of x
Mean is calculated as:

So, we have:




Variance is calculated as:

Calculate 




So:




Solving (d): Mean and Variance of y
Mean is calculated as:

So, we have:




Variance is calculated as:

Calculate 




So:




Solving (e): The covariance and the coefficient of correlation
Covariance is calculated as:

Calculate E(xy)

This gives:




So:




The coefficient of correlation is then calculated as:





--- approximated
Answer:
6.85 is the answer to this.
Step-by-step explanation:
356*24*60=525,600 minutes in a year
Birth rate
3,600,000/525,600 = 6.85
Answer:
125
Step-by-step explanation:
45 ÷9=5
5² or 5×5=25
25×5=125
Hope this helps!
The image for this is attached for reference. This problem can be used by the Pythagorean equation. To make solving convenient, let us see only one part of the tent. Hence, one side is half of the tend width which is 16/2ft. Height is 12 ft. The unknown side is the hypotenuse. The answer is:
First, we can choose the seats for the four mathematicians. Then we seat the physicits, then the engineer. There are 4! ways to seat the mathematicians, then 3! ways to seat the physicists, then 1! ways to seat the engineer. But then we must divide by 8, because we can rotate the table, so there are 8!*4!*3!/8 = 725760 ways to seat everyone.