Let X = ( X1, X2, X3, ,,,, Xn ) is iid,
f(x, a, b) =...
Let X = ( X1, X2, X3, ,,,, Xn ) is iid,
f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b
< 1
then,
Show the density of the statistic T = X(n) is given by
FX(n) (x) = n/ab * (x/a)^{n/(b-1}} for 0 <= x <=
a ; otherwise zero.
# using the following
P (X(n) < x ) = P (X1 < x, X2 < x, ,,,,,,,,, Xn < x
),
Then assume...
Let x1, x2, x3 be real numbers. The mean, x of these three
numbers is defined...
Let x1, x2, x3 be real numbers. The mean, x of these three
numbers is defined
to be
x = (x1 + x2 + x3)/3
.
Prove that there exists xi with 1 ≤ i ≤ 3 such that
xi ≤ x.
Determine the multiplicative inverse of x3 +
x2 + 1 in GF(24), using the prime (irreducible)...
Determine the multiplicative inverse of x3 +
x2 + 1 in GF(24), using the prime (irreducible)
polynomial m(x) = x4 + x + 1 as the modulo polynomial.
(Hint: Adapt the Extended Euclid’s GCD algorithm, Modular
Arithmetic, to polynomials.)
Define a sequence (xn)n≥1 recursively by x1 = 1, x2 = 2, and xn
= ((xn−1)+(xn−2))/...
Define a sequence (xn)n≥1 recursively by x1 = 1, x2 = 2, and xn
= ((xn−1)+(xn−2))/ 2 for n > 2. Prove that limn→∞ xn = x exists
and find its value.
I am trying to understand why the polynomial
x4+x3+x2+x+1 generates 5 periods
in LFSR. If we...
I am trying to understand why the polynomial
x4+x3+x2+x+1 generates 5 periods
in LFSR. If we start with 0 0 0 1 it will generate 1 0 0 0, 1 1 0
0, 0 1 1 0, and 0 0 1 1 before repeating itself again. My question
is, why does it go from 1 0 0 0 to 1 1 0 0? Shouldn't it go from 1
0 0 0 to 0 1 0 0? Thanks.
Rudin Ch 3 No 16. Fix a positive number α. Choose x1 > √ α,
and...
Rudin Ch 3 No 16. Fix a positive number α. Choose x1 > √ α,
and define a sequence x2, x3,. . . by the recursion formula x n+1 =
1 2 (xn + α /xn ). (a) Prove that xn decreases monotonically and
that lim n→∞ xn = √ α. Explain how we know xn decreases. Explain
the term monotonically