Hi,
T is a function,
where, X are i.i.d Bernoulli r.v
The end point of the derivation is,
 \le e^{-az} \left(\frac{e^{\frac{a}{\sqrt{n}}}+e^{\frac{-a}{\sqrt{n}}}}{2}\right)^n)
I am given,
, so
![Prob(T \ge z) \le e^{-az} (Expectation[e^{\frac{a.X_i}{\sqrt{n}}}])](http://latex.codecogs.com/png.latex?Prob(T \ge z) \le e^{-az} (Expectation[e^{\frac{a.X_i}{\sqrt{n}}}]) )
From a previous step, I know that Prob(X = 1) = 0.5, and Prob(X = -1) = 0.5
So the Expected values are
for X = 1, and
for X=-1
So the=
At this point it looks like the answer should be
)
I can't see where the nth power around the brackets should come from.
ie.^n)
Any ideas?
You're close! Except you missed one thing - observe the quoted text: when you plugged in your expression for what T equals, you inputtedOriginally Posted by notgoodatmath
Hi,
I am given,
instead of
. That would give you the result for one of such random variable, not but n independently identically distributed of such random variables! Thus, accounting for the one missing component, we should instead have:
And there is your power of n!
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