Question

?_{1}=[Σ^{n}?=1 ( ?_{i} −?̅ ) (
?_{i}−?̅ ) / ???] = Σ^{n}?=1 ?? ( ?_{i}−?̅
),?ℎ??? [?_{i}= (?_{i} −?̅ ) / ???]

We can prove: ?_{1} =Σ^{n}?=1 ???? ?ℎ??? ??
????????? ?????.

????? ?ℎ? ?????????

(?) Σ^{n}?=1 ?? =0

(?) Σ^{n}?=1 ?? ?? =1

(?) ?(?_{1})= ?_{1}

(?) Σ^{n}?=1 ?_{i}^{2} = (1 / ???)

(?) ???(?_{1}) =?^{2} / ???; ????:
???(?_{i})=?^{2}

Answer #1

Suppose the impulse responses of ℎ?[?] is given as:
ℎ1 = 0.7?−1?[? − 1]
(a) Is ℎ?[?] stable? Justify your answer.
(b) If it is required that ℎ[?] = 0.7??[?], find ℎ?[?].
(c) Based on your answer in (b), if ?[?] = ?[? − 1] + 2?[? − 2] +
3?[? − 3].
Find ?[?] and write it in terms of ℎ?[?].
(d) If ?[?] = ?[?] + ?[? − 1] − 2?[? − 2] is the input to this...

????? ?ℎ?? sin(?) = −2/√28 ,??? ? ?? ?? ?ℎ? 4?ℎ ????????, ????
????? ?????? of:
a) cos A
b) tan A
c) sin 2A
d) cos 2A
e) tan 2A

Using MATLAB, plot the vector field
? ⃗ = y2? ̂ − ??
̂ ??
?ℎ? ?????? − 2 < ? < +2 ??? − 2 < ? < +2
Find the magnitude of the vector field at the point
(?0,?0) = (3,2).

Consider the sample space consisting of the letters of the
alphabet {?,?,?,?,?,?,?,ℎ,?,?}. Furthermore define the events
?={?,?,?,?,?}; ?={?,?,ℎ,?} Find the probability of: i. ? ii. ? iii.
?∩? iv. ?∪?

Prove that f(x)=x*cos(1/x) is continuous at x=0.
please give detailed proof. i guess we can use squeeze
theorem.

????? ?ℎ?? ? = 5 − 2?, ??? ? = 8 + 7?, ????????:
a) ??̅
b )?/?
c) (?̅−??)/(?+?+?)

Using
MATLAB/OCTAVE, plot the vector field ?⃗=?2?̂−??̂ ?? ?ℎ?
??????−2<?<+2 ???−2<?<+2
Find
the magnitude of the vector field at the point (?0,?0)=(3,2).

Problem 3 . Suppose elements a[i] and a[i+k] are in the
wrong order and we swap them. Prove that this will remove at least
1 inversion but at most 2k − 1 inversions. (This is textbook
problem 7.3.) Further explain why both the lower bound of 1 and the
upper bound of 2k − 1 can be attained for any i, k, where k >
0

Consider the density function:
?(?) = {
6?(1 − ?) 0 < ? < 1 0 ?????ℎ???
i) Find ? and ?. ii) Compute ?(? − ? < ? < ? + ?)

Let X = [0, 1) and Y = (0, 2).
a. Define a 1-1 function from X to Y that is NOT onto Y . Prove
that it is not onto Y .
b. Define a 1-1 function from Y to X that is NOT onto X. Prove
that it is not onto X.
c. How can we use this to prove that [0, 1) ∼ (0, 2)?

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