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All of the questions relate, in one way or another, to the following process, which uses a standard 52-card deck: Step 1. Shuffle the deck throughly. Step 2. Draw a card from the deck. Step 3. Record which card was drawn. Step 4. Replace the card in the deck. Step 5. Go to step 1. :-) Yes, the process never ends 1. The random variable H counts the number of ♡s that turn up in the first 12 iterations of the process. What are P(H = 4), E(H), and V(H)? 2. The random variable Z returns a number for the card drawn on the forty-first iteration of the process: 0 if it is a ♡, 1 if it is a ◊, 3 if it is a ♣, and 4 if it is a ♣. What are P(1 ≤ Z ≤ 3), E(Z), and V(Z)? 3. The random variable W counts the number of iterations of the process required to have an ace (i.e. A♡, A◊, A♣, or A♣) turn up for the first time. What are P(W = 4), E(W), and V(W)? 4. The random variable D counts the number of iterations of the process required to have a ◇ turn up for the fourth time. What are P(D = 4), E(D), and V(D)? 5. The random variable XÊ, where k ≥ 1, counts the number times a or turns up in in the 100(k − 1) + 1st through the 100kth iterations of the process. The random variable Y returns n if Xñ > 50, but Xk ≤ 50 for all k with 1 ≤ k < n. What are P(Y = 3), E(Y), and V(Y)?

All of the questions relate, in one way or another, to the following process, which uses a standard 52-card deck: Step 1. Shuffle the deck throughly. Step 2. Draw a card from the deck. Step 3. Record which card was drawn. Step 4. Replace the card in the deck. Step 5. Go to step 1. :-) Yes, the process never ends 1. The random variable H counts the number of ♡s that turn up in the first 12 iterations of the process. What are P(H = 4), E(H), and V(H)? 2. The random variable Z returns a number for the card drawn on the forty-first iteration of the process: 0 if it is a ♡, 1 if it is a ◊, 3 if it is a ♣, and 4 if it is a ♣. What are P(1 ≤ Z ≤ 3), E(Z), and V(Z)? 3. The random variable W counts the number of iterations of the process required to have an ace (i.e. A♡, A◊, A♣, or A♣) turn up for the first time. What are P(W = 4), E(W), and V(W)? 4. The random variable D counts the number of iterations of the process required to have a ◇ turn up for the fourth time. What are P(D = 4), E(D), and V(D)? 5. The random variable XÊ, where k ≥ 1, counts the number times a or turns up in in the 100(k − 1) + 1st through the 100kth iterations of the process. The random variable Y returns n if Xñ > 50, but Xk ≤ 50 for all k with 1 ≤ k < n. What are P(Y = 3), E(Y), and V(Y)?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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All of the questions relate, in one way or another, to the following process, which uses a standard 52-card deck: Step 1. Shuffle the deck throughly. Step 2. Draw a card from the deck. Step 3. Record which card was drawn. Step 4. Replace the card in the deck. Step 5. Go to step 1. Yes, the process never ends :-) 1. The random variable H counts the number of ♡s that turn up in the first 12 iterations of the process. What are P(H = 4), E(H), and V(H)? 2. The random variable Z returns a number for the card drawn on the forty-first iteration of the process: 0 if it is a ♡, 1 if it is a ◊, 3 if it is a ♣, and 4 if it is a ♣. What are P(1 ≤ Z ≤ 3), E(Z), and V(Z)? 3. The random variable W counts the number of iterations of the process required to have an ace (i.e. A♡, A◊, or A♣) turn up for the first time. What are P(W = 4), E(W), and V(W)? 4. The random variable D counts the number of iterations of the process required to have a ◊ turn up for the fourth time. What are P(D = 4), E(D), and V(D)? 5. The random variable Xk, where k ≥ 1, counts the number times a or turns up in in the 100(k − 1) + 1st through the 100kth iterations of the process. The random variable Y returns n if Xn > 50, but Xk ≤ 50 for all k with 1 ≤ k < n. What are P(Y = 3), E(Y), and V(Y)?
Transcribed Image Text:All of the questions relate, in one way or another, to the following process, which uses a standard 52-card deck: Step 1. Shuffle the deck throughly. Step 2. Draw a card from the deck. Step 3. Record which card was drawn. Step 4. Replace the card in the deck. Step 5. Go to step 1. Yes, the process never ends :-) 1. The random variable H counts the number of ♡s that turn up in the first 12 iterations of the process. What are P(H = 4), E(H), and V(H)? 2. The random variable Z returns a number for the card drawn on the forty-first iteration of the process: 0 if it is a ♡, 1 if it is a ◊, 3 if it is a ♣, and 4 if it is a ♣. What are P(1 ≤ Z ≤ 3), E(Z), and V(Z)? 3. The random variable W counts the number of iterations of the process required to have an ace (i.e. A♡, A◊, or A♣) turn up for the first time. What are P(W = 4), E(W), and V(W)? 4. The random variable D counts the number of iterations of the process required to have a ◊ turn up for the fourth time. What are P(D = 4), E(D), and V(D)? 5. The random variable Xk, where k ≥ 1, counts the number times a or turns up in in the 100(k − 1) + 1st through the 100kth iterations of the process. The random variable Y returns n if Xn > 50, but Xk ≤ 50 for all k with 1 ≤ k < n. What are P(Y = 3), E(Y), and V(Y)?
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