Help with 4.34 - 4.41 please **Homework #4****Use the following probability model for the next 4 questions.**We define each state by using two codes. For the first part, A or B. For the second part, an integer between 1 and 3.| State s | Probability P(s) | Realization X(s) | Realization Y(s) ||---------|------------------|------------------|------------------|| A1 | 0.1 | 50 | 20 || A2 | 0.2 | 20 | 20 || A3 | 0.a | 20 | 50 || B1 | b | 50 | 50 || B2 | 0.2 | 20 | 50 || B3 | 0.1 | 50 | 20 |Suppose that P({the first part of codes = A} | {the second part of codes = 3}) = 0.75.**Question 4.34. What is (a, b)?**- a. (0.20, 0.20)- b. (0.25, 0.15)- c. (0.30, 0.10)- d. (0.35, 0.05)**Question 4.35. Which of the following is true?**- a. E(X) > E(Y)- b. E(X) < E(Y)- c. E(X + Y) = 0- d. E(X – Y) = 0**Question 4.36. What is Cov(3X, 2Y)?**- a. 9- b. 18- c. 27- d. 54 **Homework #4****Question 4.37.** What is $ E(X|Y = 50) + E(Y|X = 50) $?a. 30 b. 90 c. 60 d. 120 ---**Use the following information for the next 4 questions:**Suppose we have three random variables $ X, Y, $ and $ Z $. $ X $ is independent of both $ Y $ and $ Z $.- $ \text{Var}(Y) = 10 $ - $ \text{Var}(Z) = 16 $ - $ \text{Var}(Y + Z) = 20 $ - $ \text{Cov}(X + Y, X + Z) = 22 $ **Question 4.38.** What is $ SD(X) $?a. 5 b. 10 c. 20 d. 25 ---**Question 4.39.** What is $ SD(\sqrt{2}X + \sqrt{5}Y) $?a. 5 b. 10 c. 20 d. 25 ---**Question 4.40.** Which of the following is equal to $ \text{Cov}(X + Y, Y + Z) + \text{Cov}(X + Z, Y + Z) $?a. $ \text{Var}(Y) $ b. $ \text{Var}(Z) $ c. $ \text{Var}(Y + Z) $ d. $ \text{Cov}(Y, Z) $ ---**Question 4.41.** What is $ \text{Var}(\frac{1}{3}(X + Y + Z)) $?a. 5 b. 15 c. 25 d. 45

Name: Help with 4.34 - 4.41 please **Homework #4****Use the following probab
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Help with 4.34 - 4.41 please **Homework #4****Use the following probability model for the next 4 questions.**We define each state by using two codes. For the first part, A or B. For the second part, an integer between 1 and 3.| State s | Probability

Answered: Use the following probability model for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

Help with 4.34 - 4.41 please

**Homework #4**

**Question 4.37.** What is $ E(X|Y = 50) + E(Y|X = 50) $?

a. 30
b. 90
c. 60
d. 120

---

**Use the following information for the next 4 questions:**

Suppose we have three random variables $ X, Y, $ and $ Z $. $ X $ is independent of both $ Y $ and $ Z $.

- $ \text{Var}(Y) = 10 $
- $ \text{Var}(Z) = 16 $
- $ \text{Var}(Y + Z) = 20 $
- $ \text{Cov}(X + Y, X + Z) = 22 $

**Question 4.38.** What is $ SD(X) $?

a. 5
b. 10
c. 20
d. 25

---

**Question 4.39.** What is $ SD(\sqrt{2}X + \sqrt{5}Y) $?

a. 5
b. 10
c. 20
d. 25

---

**Question 4.40.** Which of the following is equal to $ \text{Cov}(X + Y, Y + Z) + \text{Cov}(X + Z, Y + Z) $?

a. $ \text{Var}(Y) $
b. $ \text{Var}(Z) $
c. $ \text{Var}(Y + Z) $
d. $ \text{Cov}(Y, Z) $

---

**Question 4.41.** What is $ \text{Var}(\frac{1}{3}(X + Y + Z)) $?

a. 5
b. 15
c. 25
d. 45

Expert Solution

Step 1

Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately.

4.34

From the condition,

$\sum p_{i} = 1 0.1 + 0.2 + a + b + 0.2 + 0.1 = 1 0.6 + a + b = 1 a + b = 0.4$

Given

$P (A | 3) = 0.75 \frac{P (A 3)}{P (3)} = 0.75 \frac{a}{P (A 3) + P (B 3)} = 0.75 \frac{a}{a + 0.1} = 0.75 a = 0.75 a + 0.075 0.25 a = 0.075 a = 0.3$

$a + b = 0.4 0.3 + b = 0.4 b = 0.1$

Thus, the correct option is c) (0.3, 0.1).

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions