Let X =( X1,
X2, X3 ) have the joint pdf
f(x1, x2,
x3)=60x1x22, where
x1...
Let X =( X1,
X2, X3 ) have the joint pdf
f(x1, x2,
x3)=60x1x22, where
x1 + x2 + x3=1 and
xi >0 for i = 1,2,3. find the
distribution of X1 ? Find
E(X1).
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 ,
X4 be a random sample of size 4 from...
Let X1 , X2 , X3 ,
X4 be a random sample of size 4 from a geometric
distribution with p = 1/3.
A) Find the mgf of Y = X1 + X2 +
X3 + X4.
B) How is Y distributed?
Let A be an m×n matrix, x a vector in Rn, and b a vector in...
Let A be an m×n matrix, x a vector in Rn, and b a vector in Rm.
Show that if x1 in Rn is a solution to Ax=b and x2 is a solution to
Ax=⃗0, then x1 +x2 is a solution to Ax=b.
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.
Let x1, x2, ..., xk be linearly independent vectors in R n and
let A be...
Let x1, x2, ..., xk be linearly independent vectors in R n and
let A be a nonsingular n × n matrix. Define yi = Axi for i = 1, 2,
..., k. Show that y1, y2, ..., yk are linearly independent.
How many solutions are there to equation x1 + x2 + x3 + x4 = 15...
How many solutions are there to equation x1 + x2 + x3 + x4 = 15
where xi , for i = 1, 2, 3, 4, is a nonnegative integer and
(a) x1 > 1?
(b) xi ≥ i, for i = 1, 2, 3, 4?
(c) x1 ≤ 13?
Let x1, . . . , xk be n-vectors, and
α1, . . . , αk...
Let x1, . . . , xk be n-vectors, and
α1, . . . , αk be numbers, and consider the
linear combination z = α1x1 + · · · +
αkxk.
Suppose the vectors are uncorrelated, which means that for i not
equal to j, xi and xj are uncorrelated. Show
that std(z) = sqrt(α12
std(x1)2 + · · · + αk2
std(xk)2).
Let X1, X2, X3 be a random sample of size 3 from a distribution
that is...
Let X1, X2, X3 be a random sample of size 3 from a distribution
that is Normal with mean 9 and variance 4.
(a) Determine the probability that the maximum of X1; X2; X3
exceeds 12.
(b) Determine the probability that the median of X1; X2; X3 less
than 10.
Please I need a solution that uses the pdf/CDF of the
corresponding order statistics.