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Paha777 [63]
3 years ago
13

Sum of the second and third consecutive odd integers, simplified

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
3 0
If you know how to solve word problems involving the sum of consecutive even integers, you should be able to easily solve word problems that involve the sum of consecutive odd integers. The key is to have a good grasp of what odd integers are and how consecutive odd integers can be represented.

Odd Integers

If you recall, an even integer is always
2
2 times a number. Thus, the general form of an even number is
n
=
2
k
n=2k, where
k k is an integer.
If I am incorrect I am so sorry.:(
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\frac{1}{(2k)!} E[X^{2k}] t^{2k}=\frac{1}{k!} (\frac{t^2}{2})^k =\frac{1}{2^k k!} t^{2k}

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E[X^{2k}]=\frac{(2k)!}{2^k k!}, k=0,1,2,...

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Var(X^2) = E[X^4]-[E(X^2)]^2

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E[X^4]= \frac{4!}{2^2 2!}= 3

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