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2 years ago

Solve the following compound inequality 4

Mathematics

1 answer:

CaHeK987 [17]2 years ago

7 0

Answer:

$0 < x < 8$

Step-by-step explanation:

Given

$4 < x + 4 < 12$

Required

Solve

$4 < x + 4 < 12$

Split:

$4 < x + 4$ and $x + 4< 12$

Collect Like Terms

$4 - 4 < x$ and $x < 12- 4$

$0$ and $x < 8$

Combine

$0 < x < 8$

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koban [17]

The expected length of code for one encoded symbol is

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha\ell_\alpha$

where $p_\alpha$ is the probability of picking the letter $\alpha$ , and $\ell_\alpha$ is the length of code needed to encode $\alpha$ . $p_\alpha$ is given to us, and we have

$\begin{cases}\ell_w=1\\\ell_x=2\\\ell_y=\ell_z=3\end{cases}$

so that we expect a contribution of

$\dfrac12+\dfrac24+\dfrac{2\cdot3}8=\dfrac{11}8=1.375$

bits to the code per encoded letter. For a string of length $n$ , we would then expect $E[L]=1.375n$ .

By definition of variance, we have

$\mathrm{Var}[L]=E\left[(L-E[L])^2\right]=E[L^2]-E[L]^2$

For a string consisting of one letter, we have

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha{\ell_\alpha}^2=\dfrac12+\dfrac{2^2}4+\dfrac{2\cdot3^2}8=\dfrac{15}4$

so that the variance for the length such a string is

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2 years ago

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mixas84 [53]

The answer would be 3/7

Explanation:
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