1. Consider a six-faced die whose faces have respective colours red, red, red, blue, blue, green....
1. Consider a six-faced die whose faces have respective colours red, red, red, blue, blue, green.
(a) Describe the random variable (i.e. possible outcomes and probability distribution) of a fair die throw (i.e. one where each face ends up on top with equal likelihood).
(b) What is the entropy of the random variable of part (a)?
(c) Suppose two identical such dice are thrown simultaneously. What is the probability that
i. both dice come up red?
ii. the dice come up red and blue?
iii. the dice come up red and some colour other than red?
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1. Consider a six-faced die whose faces have respective colours
red, red, red, blue, blue, green....
A die means a standard cube whose faces are numbered 1, ..., 6 and each has...
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Part I - Throwing a Dice with Six Faces (32 points) Consider a dice with six...
Part I - Throwing a Dice with Six Faces (32 points) Consider a dice with six faces, i.e. a standard dice. The possible outcomes after throwing the dice once are 1, 2,3, 4,5,6 (a) Assume that the dice is thrown once. Let w represents the outcome. Explain why P(w-i) for i = i..6, when the dice is fair (b) The fair dice is thrown twice. Find the probability of occurance of at least one 6 The fair dice is thrown...
A red die and a blue die are thrown. Let S be a random variable that...
A red die and a blue die are thrown. Let S be a random variable that denotes the square of the difference between the two numbers on the dice. For example, if the red die comes up 2 and the blue die comes up 5, then S = (2 – 5)2 = 9. What is the distribution over S? 0 (0,5/36), (1,5/18), (4,4/18), (9,3/18), (16, 2/18), (25, 1/18) O (0,5/36), (1, 4/18), (4, 3/18), (9,2/18), (16, 1/18), (25, 1/18) 0...
1) Suppose a bag contains 50 red balls, 30 green balls and 20 blue balls. (a)...
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1. We have a bag with 10 red marbles, 3 blue marbles and 5 green marbles in it. What is the probability of randomly selecting a green marble from the bag? 2. If a number is randomly chosen from the following list, what is the probability that the number is a multiple of 4? [32, 49, 55, 30, 56, 28, 50, 40, 40, 45.3.25) 3. In a single throw of two fair dice, what is the probability that a doublet...
Please show all work so I can learn <3 XOXO I would appreciate it alot ;)...
Please show all work so I can learn <3 XOXO I would
appreciate it alot ;)
1 Random Variables Consider the probability space (2, A, P) defined as follows: .A-2. i.e., the event space is the power set of Ω; P(R)1/3, P(G) P(B) PY-2/9, where we define the probability only for the clementary outcomes, and the probability of every event in A can be deduced from these valucs (as per discussion in section A.5) This probability space can model, for...
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1. A standard six-sided die is rolled. What is the probability of rolling a number greater than 3? Express your answer as a simplified fraction or a decimal rounded to four decimal places. Answer: ____________________ 2. A box contains 48 red marbles, 53 white marbles, and 67 blue marbles. If a marble is randomly selected from the box, what is the probability that it is blue? Express your answer as a simplified fraction or a decimal rounded to four decimal...
Part I - Throwing a Dice with Six Faces (32 points) Consider a dice with six faces, i.e. a standard dice. The possible outcomes after throwing the dice once are 1, 2,3, 4,5,6 (a) Assume that the dice is thrown once. Let w represents the outcome. Explain why P(w-i) for i = i..6, when the dice is fair (b) The fair dice is thrown twice. Find the probability of occurance of at least one 6 The fair dice is thrown...
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1. We have a bag with 10 red marbles, 3 blue marbles and 5 green marbles in it. What is the probability of randomly selecting a green marble from the bag? 2. If a number is randomly chosen from the following list, what is the probability that the number is a multiple of 4? [32, 49, 55, 30, 56, 28, 50, 40, 40, 45.3.25) 3. In a single throw of two fair dice, what is the probability that a doublet...
Please show all work so I can learn <3 XOXO I would
appreciate it alot ;)
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