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S2 June 2013 q9

I don't understand why obtaining the value 8.4126 and 8.8440 by subsitituting in 8.5 and 8.6 shows that the solution is between 8.5 and 8.6, also how do I choose which lambda to sub in?(the one in the equation or the one equal to the equation?)

Unrelated but also in this paper, how do you show variance in graphs of continuous random variable? image.png
Original post by Christina Tiana
I don't understand why obtaining the value 8.4126 and 8.8440 by subsitituting in 8.5 and 8.6 shows that the solution is between 8.5 and 8.6, also how do I choose which lambda to sub in?(the one in the equation or the one equal to the equation?)

Unrelated but also in this paper, how do you show variance in graphs of continuous random variable? image.png


In part 9iii) You had to show that
Unparseable latex formula:

\lambda = 0.12e^k^\lambda



If you use
Unparseable latex formula:

e^-^\lambda. \frac{\lambda^2}{2!} = 0.0072



and rearrange to find put it in the form
Unparseable latex formula:

\lambda = 0.12e^k^y

Spoiler

then substitute λ=8.5\lambda = 8.5 and λ=8.6\lambda = 8.6

when you substitute
Unparseable latex formula:

\lamdba = 8.5


LHS<RHS LHS < RHS
adn when you substitute λ=8.6\lambda = 8.6
LHS>RHS LHS > RHS
So there exists a value of λ\lambda between 8.5 and 8.6 such that LHS=RHS LHS = RHS
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Avatar for Zacken
Zacken
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Original post by Christina Tiana
I don't understand why obtaining the value 8.4126 and 8.8440 by subsitituting in 8.5 and 8.6 shows that the solution is between 8.5 and 8.6, also how do I choose which lambda to sub in?(the one in the equation or the one equal to the equation?)

Unrelated but also in this paper, how do you show variance in graphs of continuous random variable?


Do you remember your C3 stuff? Finding the roots of equations by numerical methods? One of them was showing that f(a)<0f(a) <0 and f(b)>0f(b) > 0 then there must exist a root between a and b? This is the same thing.
Original post by Zacken
Do you remember your C3 stuff? Finding the roots of equations by numerical methods? One of them was showing that f(a)<0f(a) <0 and f(b)>0f(b) > 0 then there must exist a root between a and b? This is the same thing.


Yes I thought it was a numerical method but I didnt get a sign change, and I actually am quite confused on the topic anyway so I didn't get it, thank you!

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