ANSWER:
E[X] ≈ m ln m
STEP-BY-STEP EXPLANATION:
Hint: Let X be the number needed. It is useful to represent X by
m
X = ∑ Xi
i=1
where each Xi is a geometric random variable
Solution: Assume that there is a sufficiently large number of coupons such that removing a finite number of them does not change the probability that a coupon of a given type is draw. Let X be the number of coupons picked
m
X = ∑ Xi
i=1
where Xi is the number of coupons picked between drawing the (i − 1)th coupon type and drawing i th coupon type. It should be clear that X1 = 1. Also, for each i:
Xi ∼ geometric 
P r{Xi = n} =
Such a random variable has expectation:
E [Xi
] =
= 
Next we use the fact that the expectation of a sum is the sum of the expectation, thus:
m m m m
E[X] = E ∑ Xi = ∑ E Xi = ∑ = m ∑ 
= mHm
i=1 i=1 i=1 i=1
In the case of large m this takes on the limit:
E[X] ≈ m ln m
Answer:
<em>XY = 92 units</em>
Step-by-step explanation:
<u>Similar Shapes</u>
Two shapes are similar if all their corresponding side measures are in the same proportion.
The triangles UVW and YVX are similar because their side lengths are in the proportion 1:2, given the tick marks provided in the drawing.
This means that the measure of VX is twice the measure of VW,
The measure of YV is twice the measure of UV
The measure of XY is twice the measure of UW
This last proportion gives the equation:
z + 46 = 2z
Solving for z:
z = 46
Thus, XY = z+46 = 92
XY = 92 units
Answer: C) 3
To get mean deviation it is nessasary to get the number between the two center numbers
The speed the water level rising 250 min after the filling begins
is 1/500 m/min and it will take
2000 minutes to fill the pool. I am hoping that these answers
have satisfied your queries and it will be able to help you, and if you would
like, feel free to ask another question.
Answer:
-3b - 21
Step-by-step explanation:
You have distribute the -3 to both b and 7. So, you would have to multiply the -3 to both b and 7.
