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1 vote

The equation that fits the points, with only positive terms

If you know you want to have a quadratic, call it $ax^2 + bx + c$. Then, the 3 points give you 3 simultaneous equations: $$0.2 = c$$ $$1 = 50^2 a + 50b + c$$ $$5 = 100^2 a + 100b + c$$ Clearly, the ...
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“Odd Person Out” coin flip problem and calculating expected value

Note that your expression for P[X=$n$] is of the form $\alpha \cdot \beta^{n-1}$, where $\alpha = 0.3125$ and $\beta = 0.6875$. Then $$\begin{align} \text{E[X]} &= 1 \cdot \text{P}[1] + 2 \cdot \...
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1 vote

“Odd Person Out” coin flip problem and calculating expected value

On a particular flip, there are clearly $2^5=32$ possible outcomes. Five of these will have a heads odd-one-out and five will have tails odd-one-out. Hence, the fraction $\frac{10}{32}=0.3125$ is the ...
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What is the probability of given data with the Negative binomial distribution?

To answer the question as the "real answer" you will have to: Make $100$ random variables between $0$ and $1$. Check for every number of $i$ in $\text{NegBin}(r,p)$, where $u > \text{...
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