Question

...............................................................................................................................................................................................................................................................

...........................................................................................................................................................................................................................................................................................

Let T1, T2, T3, and T4 be four independent events.

a) Provided that P(T3) > 0, show that T4 and T2 are conditionally independent given T3?

b) Provided that P(T3 ∩ T4) > 0, prove that P(T1 ∪ T2 | T3 ∩ T4) = P(T1 ∪ T2)

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Given T1, T2, T3 and T4 are independent events.

(a) Given, P(T3)>0

We have to prove that P(T4|T3)= P(T4) and also P(T2|T3)= P(T2)

( since T4 and T3 are independent.)

Here we proved that T4 and T2 are conditionally independent given T3.

(b) Given, , we have to prove that

P(T1 ∪ T2 | T3 ∩ T4) = P(T1 ∪ T2)

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Assume 4 teams, labelled T1, T2, T3, T4, compete in a tournament. Assume that the probability...
Assume 4 teams, labelled T1, T2, T3, T4, compete in a tournament. Assume that the probability of winning a game is random. Team T1 beats any team it plays with probability p > 1/2. Teams T2, T3, and T4 have the same probability q = 1/2 of beating each other and probability (1 − p) of being team T1. If team T1 plays T2 and team T3 plays T4, and the winner of each game play in the finals, what...
1.- Show that T4 = ⇒ T31 = ⇒ T3 =⇒ T2 = ⇒ T1 =⇒...
1.- Show that T4 = ⇒ T31 = ⇒ T3 =⇒ T2 = ⇒ T1 =⇒ T0. 14. Give examples of: (a) A topological space that is T0 but not T1. (b) A topological space that is T1 but not T2. (c) A topological space that is T2 but not T3.
Use the following expressions for left and right sums left sum = f(t0)Δt + f(t1)Δt +...
Use the following expressions for left and right sums left sum = f(t0)Δt + f(t1)Δt + f(t2)Δt +    + f(tn − 1)Δt right sum = f(t1)Δt + f(t2)Δt + f(t3)Δt +    + f(tn)Δt and the following table. t 0 4 8 12 16 f(t) 25 22 20 18 15 (a) If n = 4, what is Δt? Δt = What are t0, t1, t2, t3, t4? t0 = t1 = t2 = t3 = t4 = What are f(t0), f(t1), f(t2), f(t3),...
***Write a method in Java to Evaluate: ***For exp: object t2 has coefficient = 2.4 and...
***Write a method in Java to Evaluate: ***For exp: object t2 has coefficient = 2.4 and exponent = 3. it represents 2.4 * x^3. Then t2.evaluate(-1.5) is 2.4 * -1.5^3 which is -8.1. @TestMethodOrder(MethodOrderer.OrderAnnotation.class) public class PolyTermTest{ public static int score = 0; public static String result = ""; public static String currentMethodName = null; ArrayList methodsPassed = new ArrayList(); PolyTerm t1, t2, t3, t4; @BeforeEach public void setUp() throws Exception { currentMethodName = null; t1 = new PolyTerm(1, 1);...
Q. Write a method add(PolyTerm): Two PolyTerm objects can be added if and only if they...
Q. Write a method add(PolyTerm): Two PolyTerm objects can be added if and only if they have the same exponent. If the calling object can be added to the parameter object, return their sum, otherwise (if they can't be added), return null. For example 2x^3 + -7.3x^3 = -5.3x^3 while 2x^3 + 8x^2 should return null. (It's on JAVA) The JUnit Test for this question is: public class PolyTermTest {    public static int score = 0;    public static...
In a terrestrial ecosystem such as forest, maximum energy is in which trophic level? (a) T3...
In a terrestrial ecosystem such as forest, maximum energy is in which trophic level? (a) T3 (b) T4 (c) T1 (d) T2
In the figure, M2 has more mass than M1 and M1 has more mass than M3....
In the figure, M2 has more mass than M1 and M1 has more mass than M3. The questions refer to the magnitudes of tensions and weights. There is friction between the horizontal plane and M2 (?k ? 0). M2 is observed to travel at a constant speed. Assume that the pulleys are frictionless and have negligible mass. Select the appropriate statements to complete the following sentences. T1 is ... M1g. The magnitude of the net force on M2 is T2...
1- if an equation of motion given by ( X=2t , Y=2t+4 ) prove that the...
1- if an equation of motion given by ( X=2t , Y=2t+4 ) prove that the motion is Straight. 2- if the position of object given by ( X=3t-4t2+t3 ) a- give the position at ( t=1),( t=2 ),( t=3 ),( t=4 ) b- find the displacement between ( t1 = 0 and t2 = 4 ) c- find the average velocity between ( t1 = 2 and t2 = 4 )
Exercise: The sum of Poisson r.v.'s 1 point possible (graded) Consider a Poisson process with rate...
Exercise: The sum of Poisson r.v.'s 1 point possible (graded) Consider a Poisson process with rate λ=1. Consider three times that satisfy 0<t1<t2<t3. Let M be the number of arrivals during the interval [0,t2]. Let N be the number of arrivals during the interval [t1,t3]. Is the random variable M+N guaranteed to be Poisson?
10 What is the Present Value of the following cash flows using a 10 % discount...
10 What is the Present Value of the following cash flows using a 10 % discount rate T1 = 50 T2 = 300 T3 = 87 T4 = 400
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT