Question

If events X and Y are independent events then P(XNY)
=

Answer #1

If events X and Y are independent events then

**P(X N Y) = P(X) . P(Y)**

Example:- Consider the experiment of rolling a fair die

sample space = S ={1,2,3,4,5,6}

n=6

X : Occureance of an even number

X = {2,4,6} , m=3

P(X) = m/n = 3/6 = 1/2

Y : Occureance of a number greater than 4

Y = { 5,6}, k= 2

P(Y) = k/n = 2/6 = 1/3

P(X N Y) = P{6} = 1/6 ------1

P(X) . P(Y) = 1/2 * 1/3 = 1/6 --------2

from equation 1 and 2, we get

**P(X N Y) = P(X) . P(Y)**

Therefore X and Y are independent events

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

The events X and Y are mutually exclusive. suppose
P(X) = 0.18 and P(Y) = 0.16
What is the probability of either occurring?
What is the probability that neither will happen?

the events X and Y are mutually exclusive. Suppose P(X) = 0.13
and P(Y) = 0.11. What is the probability of either X or Y
occurring? (Round your answer to 2 decimal places.) What is the
probability that neither X nor Y will happen? (Round your answer to
2 decimal places.) Next

Let X and Y be independent Geometric(p) random variables. What
is P(X<Y)?

. X,Y are absolutely continuous, independent random variables
such that P(X ≥ z) = P(Y ≥ z) = e−z for z ≥ 0. Find the expectation
of min(X,Y )

Xand Y are independent X~G(p) , Y~G(p)
show U=X+Y follow NB(2,p)

Let X and Y be independent Geometric(p) random variables.
(a) What is P(X < Y)?
(b) What is the probability mass function of the minimum min(X,
Y )?

Given two events X,Y
with P(X)= 4/8
and P(Y)=2/4
1.What is the smallest possible value of P (X ∩ Y)?
2 What is the largest possible value, that is, find x and y
such that,
x≤ P( X ∩ Y ) ≤ y, holds and any value in the closed interval
[x,y] is possible

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

1. A and B are independent events, and P(A) = 0.5 and P(B) =
0.8.
Find P(A and B)
2. Suppose that P(A) = 0.3, P(B) = 0.4, and
P(A and B) = 0.12.
a. What is P(A|B)?
b. What is P(B|A)?
c. Are A and B independent
3) Describe in your own words why the following statements
are
correct.
a. Two events cannot be independent if they are already
known to be mutually exclusive
b. Two events cannot be...

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