If it is HT, then no matter the next one is T or H, TH already occurs before HH, right?
If it is TT, then also no matter the next one is T or H, TH already occurs before HH, right?
If it is TH, then obviously no matter the next one is T or H, TH already occurs before HH, right?
Just the case if...
Homework Statement
A fair coin is continually flipped. What is the probability that the pattern T,H occurs before the pattern H,H, where T and H respectively denote Tail and Head of a coin?
Homework Equations
Prob. = (n r) (pr)(1-p)n-r
The Attempt at a Solution
I am thinking whether the...
I understand 1st and 3rd question now.
For 2nd question,
my approach now is
let p be the P(accpetable) in 1st question.
P(more than 2 tests) = 1 - [ P(1st acceptable) + P(1st rejected, 2nd accpetable) ] = 1 - [ p + (1-p)p ]. Is this correct?
Homework Statement
Due to the pollution from the industry around an apple farm, the apples grown there may be contaminated by heavy metals. It is believed that the amount of heavy metals in an apple of the farm follows the Normal distribution.
N(16,16) which has a mean μ = 16 units and σ = √16...
Homework Statement
Given sin x = (eix - e-ix) / 2i,
I want to prove that
arcsin x = -i ln(ix + √1 - x2)
Homework Equations
I know about the Euler's formula and complex number. But I have never learnt about complex logarithms.
The Attempt at a Solution
I try to use x = sin y. But it seems...
Homework Statement
Decompose x5 - 1 into the product of 3 polynomials with real coefficients, using roots of unity.
Homework Equations
As far as I know, for xn = 1 for all n ∈ ℤ, there exist n distinct roots.
The Attempt at a Solution
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So, let ω = e2πi/5. I can therefore find all the 5th...