Let u = <3, 2, 5> and v = <-2,5,4>
Compute the angle between u and...
Let u = <3, 2, 5> and v = <-2,5,4>
Compute the angle between u and v b)
Compute proj v u
Let X1, ..., X5 ~ Gamma(1, 1), the unit
exponential distribution, and let X(1), ...,
X(5)...
Let X1, ..., X5 ~ Gamma(1, 1), the unit
exponential distribution, and let X(1), ...,
X(5) be the corresponding order statistics. Write the
densities of X(2) and X(5) and the joint
density of (X(2), X(5)). From these, compute
the probabilities P(X(2) > 2), P(X(5) <
4), and P(X(5) - X(2) > 3).
use r-studio code to compute
1. Let T ∼ t – distributed with the given degrees...
use r-studio code to compute
1. Let T ∼ t – distributed with the given degrees of freedom (df),
then compute the following probabilities with a nice little picture
beside each problem: [5 points]
(e) df = ∞, P(T > 2.3)
2. Let T ∼ t – distributed with the given degrees of freedom
(df), compute the following quantiles (percentiles) with a nice
little picture beside each problem: [5 points]
(a) df = 2, 0.05th percentile
(b) df = 7,...
Let S = {2, 6, 8, 9} and T = {1, 2, 5}. Explicitly list the...
Let S = {2, 6, 8, 9} and T = {1, 2, 5}. Explicitly list the
members of the following sets: ? ∪ ?, ? ∩ ?, ? − ?, ? × ?, ? × ?,
℘(?) and ℘(?)
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an...
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an
example of a function f: A -> A with the indicated properties,
or explain why no such function exists.
(a) f is bijective, but is not the identity function f(x) =
x.
(b) f is neither one-to-one nor onto.
(c) f is one-to-one, but not onto.
(d) f is onto, but not one-to-one.
1. Let ⃗u = −2[4,0,1]+[−1,3,−2] and ⃗v = 3[4,0,1]+5[−1,3,−2].
Let w⃗ = 3⃗u−⃗v. Express w⃗ as...
1. Let ⃗u = −2[4,0,1]+[−1,3,−2] and ⃗v = 3[4,0,1]+5[−1,3,−2].
Let w⃗ = 3⃗u−⃗v. Express w⃗ as a linear combination of the vectors
[4, 0, 1] and [−1, 3, −2].
2. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 3,
||⃗u − ⃗v|| = 5, and that⃗u.⃗v = 1. What is ||⃗v||?.
3. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 5
and that ||⃗v|| = 2. Show that ||⃗u −...