Question

several conception about independent

Q1. if two event is independent, then they are disjoint????

Q2. if two event are independent ,then P(A|B)=P(A)???

Q3. If two events are independent, then P(A intersection B)=P(A)+P(B)-0 ???

Q.4 if two events are independent, then P(A|B)=P(A)P(B) if yes, please explain why because in my textbook it should be P(A and B)=P(A)P(B)

Please follow the comments as well

Answer #1

Q1. if two event is independent, then they are disjoint????
Q2. If two events are independent, then P(A intersection
B)=P(A)+P(B)-0 ???
Q.3 if two events are independent, then P(A|B)=P(A)P(B) if yes,
please explain why because in my textbook it should be P(A and
B)=P(A)P(B)
Please follow the comments as well
Please explain organically

Conception about independent and identically distribued
in the real life explanation, for example assume the human
height is i.i.d, then random variable
E[X_bar1]=E[X_bar2]=...E[X_barn] and
X_bar=Sn/n, Sn=X1+X2...+Xn
so we draw one person, assume his height is 5ft7 then we draw 2
people, their average height will be 5ft 7, we draw 10 people and
their average height is 5ft7?? is this correct???
Please correct my conception if I am not making sense and follow
the comment as well

Conception about hypothesis test:
Q1. my professor said if the null hypothesis is true, then it is
normal distribution but what does that mean? because sometimes we
will reject the H0, does that mean if we reject it then it is not
normal distribution?
Q2. sometimes we will have H0: u=30 something like that, but I
don't understand as i was told that we don't know the population
value; however u is the population value so i am confused. Plus,...

1. Define PS to be the event that a college student owns a
Playstation 4, and X to be the event that a college student owns an
Xbox One.We know P( PS) = 0.7 and P(X) = 0.4. Are the events PS and
X Mutually Exclusive(disjoint)?
a) Yes
b) No
2. We also know P( PS|X) = 0.75. Find the probability a college
student owns both a Playstation 4 and an Xbox One. Recall that P(
PS ) = 0.7...

Q1:
a) Re-derive the inclusion-exclusion principle for two events
using only the probability axioms.
Probability axioms: Given an event A in Ω:
A1) P(A) >= 0
A2) P(Ω) = 1
A3) P(U (from i=1 to n) A_i) = Σ (from i=1 to n) P(A_i) - if
A_i's are disjoint/ mutually exclusive
Inclusion Exclusion Principle for two events: (A U B) = (A) +
(B) + (A ∩ B)
b) Then, using only the axioms and the inclusion-exclusion
principle for two...

Two spheres carrying the charge
Q1=+Q,Q2=−Q uniformly distributed across the
surface have radii R1 and R2, and their
centers are a distance dapart. We assume that
d>>R1,R2. (a) Why is this assumption
necessary? (b) Choose a coordinate axis along the direction that
connects the centers of the two spheres.Choosethe origin at the
center of sphere 1. This defines the radial direction. In unit
vector notation, what is the net electric field at some point P
between the surfaces of the...

Q1.
Which event from below is not expected to improve labor
productivity?
A.The acquisition of more education and training by the labor
force.
B.Technological advance.
C.The realization of economies of scale.
D.An increase in the size of the labor force.
Q2.
Say, you know that the labor productivity is increasing by 2
percent every year due to technology improvements. Knowing this and
keeping everything else equal, estimate the number of years for the
standards of living to double
A.35 years....

Suppose there are two firms in the market. Let Q1 be the output
of the first firm and Q2 be the output of the second. Both firms
have the same marginal costs: MC1 = MC2 = $5 and zero fixed costs.
The market demand curve is P = 53 − Q.
(a) (6 points) Suppose (as in the Cournot model) that each firm
chooses its profit-maximizing level of output assuming that its
competitor’s output is fixed. Find each firm’s reaction...

Q1 Ch1 (20%) a. Supply: Suppose the following information is
known about a market: 1. Sellers will not sell at all below a price
of $2. 2. At a price of $10, any given seller will sell 10 units.
3. There are 100 identical sellers in the market. Assuming a linear
supply curve, use this information to derive the market supply
curve. b. Demand: Suppose the demand for a particular product can
be expressed as Q = 100/p. Calculate the...

Q1.Researchers were interested in determining the relative
effectiveness of two different brands of eye drops in alleviating
the symptoms of 'dry eye syndrome'. Forty subjects, who suffered
from 'dry eye syndrome', were randomly assigned to receive either
brand A or brand B of the eye-drops - 20 subjects to each brand.
The eyedrops were administered to each subject and the time until
symptoms returned was recorded for each subject. Based on the
information provided, which of the following statement/s is...

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