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6. (a) (5 points) A 20 sided die in the shape of an icosahedron has 30...
52 68 Problem 6. (8 points) A six-sided die is loaded in a way that each...
52 68 Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome is less...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome is less...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome is less...
4. Given a semi-regular polyhedron that has a triangle, two squares and a pentagon meeting at...
4. Given a semi-regular polyhedron that has a triangle, two squares and a pentagon meeting at each vertex. Answer the following questions. (a) Calculate the angel defect at each vertex. (b) Deduce how many vertices this polyhedron must have. (c) Deduce how many triangular faces, how many square faces and how many pentagonal faces this polyhedron must have. (d) How many edges does this polyhedron have?
Draw a planar graph(with no loops or multiple edges) for each of the following properties, if...
Draw a planar graph(with no loops or multiple edges) for each of the following properties, if possible. If not possible, explain briefly why not. b) 8 vertices, all of degree 3 ( how many edges and regions must there be) c) has exactly 7 vertices, has an euler cycle and 3 is minimum vertex coloring number Also please draw the graph.
A die means a standard cube whose faces are numbered 1, ..., 6 and each has...
A die means a standard cube whose faces are numbered 1, ..., 6 and each has equal probability of being rolled. A green die and a red die are rolled simultaneously, with equal probability for each of the 36 possible outcomes. Describe the sample space. Then find the probability that: a. the sum is 7; b the sum is 11; thesumis7or11; thesumisneither7nor11; b. the same value occurs on each die; c. the value on the green die is greater than...
4. [20 Points We first examine a sequence of rolls of a four-sided die at an the observed outcome Xi E {1,2,3,4}. At ea...
4. [20 Points We first examine a sequence of rolls of a four-sided die at an the observed outcome Xi E {1,2,3,4}. At each of these times, the casino can be in one of two states z E1, 2}. When z = 1 the casino uses a fair die, while when z = 2 the die is biased so that rolling a 1 is more simple hidden Markov model (HMM). We observe a "occasionally dishonest casino", where at time likely....
3. A crate has 20 apples. Assume that they are all different in look or shape...
3. A crate has 20 apples. Assume that they are all different in look or shape (a) In how many diferent ways can 3 apples be drawn from the crate? You must write down the steps leading to your answer (b) If 2 of the 20 apples are rotten, how many of the draws in part (a) contain exactly 1 rotten apple? You must write down the steps leading to your answer. 4. To play the Powerball lottery, you have...
1. Sheila has two six-sided dice- one is purple and the other is blue. She rolls...
1. Sheila has two six-sided dice- one is purple and the other is blue. She rolls both dice and observes the following outcome-if the purple die is 5 and the blue is 1 I might use the Y5G1 to denote the observation. A. How many outcomes come up doubles- both dice have the same number? B. How many possible outcomes are there for this observation? C. Find the probability that my observation is doubles. What contextual assumption do you need...
52 68 Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome is less...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome is less...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome is less...
4. Given a semi-regular polyhedron that has a triangle, two squares and a pentagon meeting at each vertex. Answer the following questions. (a) Calculate the angel defect at each vertex. (b) Deduce how many vertices this polyhedron must have. (c) Deduce how many triangular faces, how many square faces and how many pentagonal faces this polyhedron must have. (d) How many edges does this polyhedron have?
4. [20 Points We first examine a sequence of rolls of a four-sided die at an the observed outcome Xi E {1,2,3,4}. At each of these times, the casino can be in one of two states z E1, 2}. When z = 1 the casino uses a fair die, while when z = 2 the die is biased so that rolling a 1 is more simple hidden Markov model (HMM). We observe a "occasionally dishonest casino", where at time likely....
3. A crate has 20 apples. Assume that they are all different in look or shape (a) In how many diferent ways can 3 apples be drawn from the crate? You must write down the steps leading to your answer (b) If 2 of the 20 apples are rotten, how many of the draws in part (a) contain exactly 1 rotten apple? You must write down the steps leading to your answer. 4. To play the Powerball lottery, you have...
1. Sheila has two six-sided dice- one is purple and the other is blue. She rolls both dice and observes the following outcome-if the purple die is 5 and the blue is 1 I might use the Y5G1 to denote the observation. A. How many outcomes come up doubles- both dice have the same number? B. How many possible outcomes are there for this observation? C. Find the probability that my observation is doubles. What contextual assumption do you need...
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