Summation Notation
- Thread starter AndrewP
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For problem b, what do you get when you apply the first hint to the problem?Any help with these questions is appreciated (specifically (b) and (c)), I think I'm good for question (a) but if anyone wants to try explaining it it will still be very much appreciated.
For \(\displaystyle \displaystyle \sum_{k=a}^bf(k)\), say the sum of f(k) from a through b when answering my questions.
Once you have that result, see if you can apply this rule to it:
\(\displaystyle \displaystyle \sum_{k=a}^b\{c * f(k)\} = c * \sum_{k=a}^bf(k).\)
What does applying that rule get you?
Do you now see the relevance of the second hint?
With respect to problem A, the proof involves two laws of summation and one definition.Any help with these questions is appreciated (specifically (b) and (c)), I think I'm good for question (a) but if anyone wants to try explaining it it will still be very much appreciated.
\(\displaystyle \displaystyle \left(\sum_{k=a}^bf(k) + g(k)\right) = \left(\sum_{k=a}^bf(k)\right) + \left(\sum_{k=a}^bg(k)\right).\) One law.
\(\displaystyle c\ is\ a\ constant \implies \displaystyle \sum_{k = a}^bc = c\{(b + 1) - a\}.\) Another law.
\(\displaystyle \bar X = \dfrac{1}{N}\displaystyle \sum_{i=1}^NX_i.\) Definition.
Apply those two laws and the definition, and you get a nicely formal proof.
I got an answer of i? Can you verify this?
These three questions are about summations and so do not specifically reference probabilities at all. What is the probability part of question (b) that you are referring to? Nor do teachers do give hints that are irrelevant or inapplicable. If you apply the two hints given, the solution of question b is almost mechanical. See how far you get with the first hint. As for question c, it involves one of the hints for problem b (as your teacher pointed out). So let's get question b out of the way first. Before worrying about the second hint, let's see how far you can go with the first hint for question b. What is there about question b that shows a similarity with the first hint?
You got an answer of i to what? My question did not even have an i in it.