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1025867@etusd.org
1025867@etusd.org
for question 8.25 what does the k above 2 mean in
Let P(4)=xP(4)=x. Then P(k)=24− k ⋅xP(k)=24−k⋅x for k=1,2,3,4k=1,2,3,4. As all the probabilities sum to 11, we have x+2x+4x+8x=15x=1x+2x+4x+8x=15x=1. Thus x=1/15x=1/15.
Re: 1025867@etusd.org
The problem is telling us that $P(1) = 2\cdot P(2)$, $P(2) = 2 \cdot P(3)$, and $P(3) = 2 \cdot P(4)$. This means $$\begin{aligned}P(1) &= 2^3\cdot P(4) \\ P(2) &= 2^2 \cdot P(4) \\ P(3) &= 2 \cdot P(4).\\\end{aligned}$$
In the solution, instead of writing each of these separately, we have $P(k) = 2^{4 - k} \cdot P(4)$ for $k = 1, 2, 3, 4$.
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