The moment generating function (mgf) of y is given by
Since the momoent generating function of x is given by
When p tends to 0, we have
Applying L'Hopital's rule we have:
This shows that y converges to <span>a chi squared random variable with 2r degrees of freedom</span>.
Answer:
sssssssssssssssssssssssssssssssss
Step-by-step explanation:
Basically you know that they are 2 consecutive numbers whose product is 1980.
<span>n*(n+1)=1980 </span>
<span>n^2 + n - 1980 = 0 </span>
<span>(n -44)(n + 45)= 0 </span>
<span>n=44 </span>
<span>so the 2 page numbers is 44 and 45. </span>
<span>The faster way is just to take the square root of 1980 and since that is 44.497 you can conclude that the 2 numbers is below and above it (44, 45)</span>
Answer: The hook would be 2.2 inches (approximately) above the top of the frame
Step-by-step explanation: Please refer to the picture attached for further details.
The top of the picture frame has been given as 9 inches and a 10 inch ribbon has been attached in order to hang it on a wall. The ribbon at the point of being hung up would be divided into 5 inches on either side (as shown in the picture). The line from the tip/hook down to the frame would divide the length of the frame into two equal lengths, that is 4.5 inches on either side of the hook. This would effectively give us two similar right angled triangles with sides 5 inches, 4.5 inches and a third side yet unknown. That third side is the distance from the hook to the top of the frame. The distance is calculated by using the Pythagoras theorem which states as follows;
AC^2 = AB^2 + BC^2
Where AC is the hypotenuse (longest side) and AB and BC are the other two sides
5^2 = 4.5^2 + BC^2
25 = 20.25 + BC^2
Subtract 20.25 from both sides of the equation
4.75 = BC^2
Add the square root sign to both sides of the equation
2.1794 = BC
Rounded up to the nearest tenth, the distance from the hook to the top of the frame will be 2.2 inches
Answer:
3 oatmeal muffins
Step-by-step explanation:
First, subtract the 5 muffins she dropped from the total:
73 - 5
= 68
Then, divide this by 13:
68/13
= 5.23
We need a whole number of muffins in each container, so round this down to 5.
This means that there can be 5 muffins in each of the 13 containers.
Find how many will be leftover:
5(13)
= 65
68 - 65
= 3
So, there will be 3 oatmeal muffins left