Question

1. Suppose A and B are independent events with probabilities P(A) = 1/2 and P(B) = 1/3. Define random variables X and Y by X =Ia+Ib, Y=Ia-Ib, where Ia, Ib are indicator functions (a) What is the joint distribution of X and Y? (b) What is P(X less than 2, Y greater than or equal to zero), (c) Are X and Y independent, Justify

Answer #1

Suppose events A, B, and C are MUTUALLY INDEPENDENT and P(a) =
1/4, P(B) = 1/3, and P(C) =1/2 and N denotes the total number of
events among A, B, C, that occur
(a) Draw a venn diagram
(b) What is the E(N)
(c) What is E(N^2)
(d) What is Cov(Ia,N)
(e) Find P(N <= 2 | C)
Thank you!

1. Answer the following
a. If A and B are independent events, then P(A and B) =
P(A)P(B). True or false?
b. Let A, B and C be independent events with P(A) = 0.7, P(B) =
0.8, P(CC) = 0.5. Find P(A and B and C)
c. Compute the mean and standard deviation of the random
variable with the given discrete
probability distribution:
X P(X)
-3 0.10
0 0.17
1 0.56
3 0.17

Let A be an event, and let IA be the associated indicator random
variable: IA(ω)=1 if ω∈A, and IA(ω)=0 if ω∉A. Similarly, let IB be
the indicator of another event, B. Suppose that, P(A)=p, P(B)=q,
and P(A∪B)=r.
Find E[(IA−IB)2] in terms of p,q,r?
2.Determine Var(IA−IB) in terms of p,q,r?

Independence. Suppose X and Y are independent. Let W = h(X) and
Z = l`(Y ) for some functions h and `. Make use of IEf(X)g(Y ) =
IEf(X)IEg(Y ) for all f and g greater or equal to 0 types of random
variables, not just discrete random variables. a) Show that X and Z
are independent. b) Show that W and Z are independent. c) Suppose Z
= l`(Y ) and all we know is that X and Z...

Let A be an event, and
let IA be the associated indicator random variable: IA(ω)=1 if ω∈A,
and IA(ω)=0 if ω∉A. Similarly, let IB be the indicator of another
event, B. Suppose that, P(A)=p, P(B)=q, and P(A intersection
B)=r.
Find E[(IA−IB)2] in
terms of p,q,r?
2.Determine Var(IA−IB)
in terms of p,q,r?
The solution in Chegg
is for P(AUB)=r instead of P(A intersection B)=r. I need to know
how to find Var(IA−IB) in terms of p,q,r?

1. Suppose that X 1 , X 2 and X 3 are i.i.d (i.e. independent
and identically distributed) random
variables each with mean and variance . Which of the following
three point estimators of is the “best”
point estimator? Justify your answer.
2.The mean annual salary for flight attendants is about $65,700
and the standard deviation is
$14,500. A random sample of 100 flight attendants is selected from
this population.
What is the probability that the mean annual salary of...

True or False:
10. The probability of an event is a value which must be greater
than 0 and less than 1.
11. If events A and B are mutually exclusive, then P(A|B) is always
equal to zero.
12. Mutually exclusive events cannot be independent.
13. A classical probability measure is a probability assessment
that is based on relative frequency.
14. The probability of an event is the product of the probabilities
of the sample space outcomes that correspond to...

Suppose A, B, and C are independent events with respective
probabilities 1/3, 1/4, and 1/5. What is P ( A ∩ B | C )? Express
your answer as a decimal to three decimal places.

events a,b, and c occur with respective probabilities 0.48,
0.46, and 0.24. event b is independent of the events a and c. event
b is also independent of the joint occurrence of a and c. if the
probability of the event a∩c is 0.19, compute the probability of
the event a ∪c U b.

1. Suppose that A, B are two independent events, with
P(A) = 0.3 and P(B) = 0.4.
Find P(A and B)
a. 0.12
b. 0.3
c. 0.4
d. 0.70
2. Experiment: choosing a single ball from a bag which
has equal number of red, green, blue, and white ball and then
rolling a fair 6-sided die.
a.) List the sample space.
b.) What is the probability of drawing a green ball and
even number?
2.

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