Suppose that we have a sample space with five equally likely
experimental outcomes:
E1, E2,
E3,...
Suppose that we have a sample space with five equally likely
experimental outcomes:
E1, E2,
E3, E4,
E5.
Let
A
=
{E2, E4}
B
=
{E1, E3}
C
=
{E1, E4,
E5}.
(a)
Find
P(A), P(B), and
P(C).
P(A)=
P(B)=
P(C)=
(b)
Find
P(A ∪ B).
P(A ∪ B)
(c)
Find
AC. (Enter your answers as a comma-separated
list.)
AC =
Find
CC. (Enter your answers as a comma-separated
list.)
CC =
Find
P(AC)
and
P(CC).
P(AC)
=
P(CC)
=...
Suppose that we have a sample space with six equally likely
experimental outcomes: x1, x2, x3,...
Suppose that we have a sample space with six equally likely
experimental outcomes: x1, x2, x3, x4, x5, x6, and that A = { x2,
x3, x5} and B = { x1, x2} and C= {x1, x4, x6}, then P(A ∩
B) =
Let S = { e1, e2, e3,
e4 } be the standard basis for R4 ,...
Let S = { e1, e2, e3,
e4 } be the standard basis for R4 , and let B
= { v1, v2, v3, v4, }
be the basis with vi = T(ei ), where
T ( x1, x2, x3, x4 )
= (x2, x3, x4, x1 ).
Find the transition matrices P B to S and P S to
B.
Let A⊆(X,d) a metric space. Suppose there are an infinite number
of elements in e1,e2,e3,...∈ A...
Let A⊆(X,d) a metric space. Suppose there are an infinite number
of elements in e1,e2,e3,...∈ A such that d(ei,ej)=4 if i≠j and
d(ei,ej)=0 if i=j for i,j=1,2,3...
Prove that A is not totally bounded.
(Please do not write in script and show all your steps and
definitions used)
please show work/reasoning if possible
8: An experiment has three possible elementary outcomes a, b,
and...
please show work/reasoning if possible
8: An experiment has three possible elementary outcomes a, b,
and c. Thus, the sample space is S = {a, b, c}. Define three events
E1 = {a, b}, E2 = {a, c}, and E3 = {b, c}.
Let us also define a probability measure to have values P[E1]
=2/3, P[E2] =1/3, and P[E3] =1/3.
Which one of the following derivation is wrong (or which one
best answer the nature of this question)?
A) P(E1...
Consider two events, A and B, of a sample space such that P(A) =
P(B) =...
Consider two events, A and B, of a sample space such that P(A) =
P(B) = 0.7 a).Is it possible that the events A and B are mutually
exclusive? Explain. b).If the events A and B are independent, find
the probability that the two events occur together. c).If A and B
are independent, find the probability that at least one of the two
events will occur. d).Suppose P(B|A) = 0.5, in this case are A and
B independent or dependent?...
1. Two dice are rolled. There are 36 possible outcomes, the
sample space is:
(1,1) (1,2)...
1. Two dice are rolled. There are 36 possible outcomes, the
sample space is:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4)
(2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3)
(4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2)
(6,3) (6,4) (6,5) (6,6)
A = ‘second roll is a 6’
B = ‘sum of two dice equals 7’
C = ‘sum of two dice equals 3’
a. What is P(B|A)?
b. What is...