4. Kitty generates random numbers between 1 and 6 by rolling a fair cubical die. Caleb generates random numbers between 1 and 6 by tossing a fair coin five times, counting the heads, and adding 1 to the result. Ursula generates random numbers between 1 and 6 by tossing a fair coin three times to generate a binary number with 3 bits (H = 1, T = 0). If she gets 000 or 111 she discards the result and tosses the coin 3 more times. Otherwise, she accepts the binary number resulting from the 3 tosses. Let K, C, and U be the random variables describing the outcomes of these 3 random number generators. Describe the three probability mass functions Pk, Pc, and Pu.
4. Kitty generates random numbers between 1 and 6 by rolling a fair cubical die. Caleb generates random numbers between 1 and 6 by tossing a fair coin five times, counting the heads, and adding 1 to the result. Ursula generates random numbers between 1 and 6 by tossing a fair coin three times to generate a binary number with 3 bits (H = 1, T = 0). If she gets 000 or 111 she discards the result and tosses the coin 3 more times. Otherwise, she accepts the binary number resulting from the 3 tosses. Let K, C, and U be the random variables describing the outcomes of these 3 random number generators. Describe the three probability mass functions Pk, Pc, and Pu.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Please provide a detialed answer and help to solve this in detial. I want to understand the steps involved
Transcribed Image Text:4. Kitty generates random numbers between 1 and 6 by rolling a fair cubical die.
Caleb generates random numbers between 1 and 6 by tossing a fair coin five times, counting the heads,
and adding 1 to the result.
Ursula generates random numbers between 1 and 6 by tossing a fair coin three times to generate a binary
number with 3 bits (H = 1, T = 0). If she gets 000 or 111 she discards the result and tosses the coin 3
more times. Otherwise, she accepts the binary number resulting from the 3 tosses.
Let K, C, and U be the random variables describing the outcomes of these 3 random number generators.
Describe the three probability mass functions PK, Pc, and Pu.
Expert Solution
Step 1: Kitty's number generation
Kitty generates random numbers between 1 and 6 by rolling a fair cubical die. The die has 6 faces and each face has an equal probability of 1/6 of coming.
The probability mass function (pmf) of K (where K is the number on the dice) is given as:
- P(K = 1) = 1/6
- P(K = 2) = 1/6
- P(K = 3) = 1/6
- P(K = 4) = 1/6
- P(K = 5) = 1/6
- P(K = 6) = 1/6
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