Show work, thank you!
Suppose that A1, A2 and B are events where A1 and A2...
Show work, thank you!
Suppose that A1, A2 and B are events where A1 and A2 are
mutually exclusive events and P(A1) = .5, P(A2) = .5, P(B│A1) = .9,
P(B│A2) = .2.
Find P(A2│B)
A. 0.90
B. 0.20
C. 0.50
D. 0.18
Let n∈N, and let a1,a2,...an∈R. Prove that
|a1+a2+...+an|<or=|a1|+|a2|+...+|an|
Let n∈N, and let a1,a2,...an∈R. Prove that
|a1+a2+...+an|<or=|a1|+|a2|+...+|an|
Let A1, A2, . . . , An be n independent events in a sample space...
Let A1, A2, . . . , An be n independent events in a sample space
Ω, with respective probability pi = P (Ai). Give a simple
expression for the probability P(A1 ∪A2 ∪...∪An) in terms of p1,
p2, ..., pn. Let us now apply your result in a practical setting: a
robot undergoes n independent tests, which are such that for each
test the probability of failure is p. What is the probability that
the robot fails at least...
If X, Y, and Z are independent and identically distributed
Γ(1,1), derive the joint distribution of...
If X, Y, and Z are independent and identically distributed
Γ(1,1), derive the joint distribution of U = X+Y, V = X + Z, and W
= Y + Z.
(4) Prove that, if A1, A2, ..., An are countable sets, then A1 ∪
A2 ∪...
(4) Prove that, if A1, A2, ..., An are countable sets, then A1 ∪
A2 ∪ ... ∪ An is countable. (Hint: Induction.)
(6) Let F be the set of all functions from R to R. Show that |F|
> 2 ℵ0 . (Hint: Find an injective function from P(R) to F.)
(7) Let X = {1, 2, 3, 4}, Y = {5, 6, 7, 8}, T = {∅, {1}, {4},
{1, 4}, {1, 2, 3, 4}}, and S =...
Question 3. Let a1,...,an ∈R. Prove that
(a1 + a2 + ... + an)2
/n ≤...
Question 3. Let a1,...,an ∈R. Prove that
(a1 + a2 + ... + an)2
/n ≤ (a1)2 + (a2)2 +
... + (an)2.
Question 5. Let S ⊆R and T ⊆R be non-empty. Suppose that s ≤ t for
all s ∈ S and t ∈ T. Prove that sup(S) ≤ inf(T).
Question 6. Let S ⊆ R and T ⊆ R. Suppose that S is bounded above
and T is bounded below. Let U = {t−s|t ∈ T, s...
consider a sample space defined by events a1, a2, b1 and b2
where a1 and a2...
consider a sample space defined by events a1, a2, b1 and b2
where a1 and a2 are complements .given p(a1)=0.2 p(b1/a1) = 0.5 and
p(b1/a2) =0.7 what is the probability of p (a1/b1)
P(A1/B1)=
round to the 3rd decimal