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◊, AS or A) turn up for the first time. What are P(W = 4), E(W), and V(W)?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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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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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)?
turns up
5. The random variable Xk, where k ≥ 1, counts the number times a or
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: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)? turns up 5. The random variable Xk, where k ≥ 1, counts the number times a or 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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