The survey of a group of students showed that 50 like tea,40 liked coffee,35 liked milk,20 liked coffee as well as tea,18 liked
1 answer:
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The expected length of code for one encoded symbol is
where is the probability of picking the letter
, and
is the length of code needed to encode
.
is given to us, and we have
so that we expect a contribution of
bits to the code per encoded letter. For a string of length , we would then expect
.
By definition of variance, we have
For a string consisting of one letter, we have
so that the variance for the length such a string is
"squared" bits per encoded letter. For a string of length , we would get
.
Answer:
The given function symmetric about the y-axis.
Step-by-step explanation:
The given function is
.... (1)
1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point (r,-θ ) or (-r, π - θ ) also lies on the graph.
2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,π - θ ) or (-r, -θ ) also lies on the graph.
3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.
Put (r, -θ ) in the given function.
Therefore it is not symmetric about x-axis.
Put (-r, -θ ) in the given function.
Therefore it is symmetric about y-axis.
Put (-r,θ ) in the given function.
Therefore it is not symmetric about the origin.