You throw a four sided symmetric die, if X denotes the # you get on top...
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Y = 2X - 4, perfect linear relationship with positive slope
Correlation coefficient of X and Y is 1
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throw a four sided symmetric die, if X denotes the # you get on top...
Consider a game where you roll a six-sided die and a four-sided die, then you subtract...
Consider a game where you roll a six-sided die and a four-sided die, then you subtract the number on the four-sided die from the number on the six-sided die. If the number is positive, you receive that much money (in dollars). If the number is negative, you pay that much money (in dollars). For example, you might roll a 5 on the six-sided die and a 2 on the four-sided die, in which case you would win $3. You might...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be |X-Y|. The range of Z will be from 0 to 3. 1. Find E(Z). 2. Find P(Z = 1|Z <3). 3. What is the probability that you have to play the game 4 times before you roll Z=3? 4. What is the probability...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X+Y). The range of Z will be from 2-8. 1.(2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 71Z > 5). 3.(2.5 points) What is the probability that you have to play the game 4 times before you roll Z=7? 4. (2.5...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X+Y). The range of Z will be from 2-8. 1.(2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 71Z > 5). 3.(2.5 points) What is the probability that you have to play the game 4 times before you roll Z=7? 4. (2.5...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be X-Y). The range of Z will be from 0 to 3. 1. (2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 21Z >1). 3. (2.5 points) What is the probability that you have to play the game 6 times before you roll...
Fair diced, which is unbiased. Each throw is independent. Step 1. You roll a six-sided die....
Fair diced, which is unbiased. Each throw is independent.
Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y], rounded to nearest .xx.
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X-Y). The range of Z will be from -3 to 3. 1. (2.5 points) Find E(Z). 2. (2.5 points) Find P(Z =-1|Z < 1). 3. (2.5 points) What is the probability that you have to play the game 3 times before you roll...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X-Y). The range of Z will be from -3 to 3. 1. (2.5 points) Find E(Z). 2. (2.5 points) Find P(Z =-1|Z < 1). 3. (2.5 points) What is the probability that you have to play the game 3 times before you roll...
Suppose you have a six sided die. One face is printed with the number 1. Two faces...
Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C_1, C_2, and C_3. C_1 will land Heads with probability 1/5. C_2 will land Heads with probability 1/3. C_3 will land Heads with probability 1/2. You roll the die. If the die lands with a 1 face up, flip coin C_1 If the die lands with...
Suppose you have a six sided die. One face is printed with the number 1. Two...
Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C_1, C_2, and C_3. C_1 will land Heads with probability 1/3. C_2 will land Heads with probability 1/5. C_3 will land Heads with probability 1/4. You roll the die. If the die lands with a 1 face up, flip coin C_1 If the die...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X+Y). The range of Z will be from 2-8. 1.(2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 71Z > 5). 3.(2.5 points) What is the probability that you have to play the game 4 times before you roll Z=7? 4. (2.5...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X+Y). The range of Z will be from 2-8. 1.(2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 71Z > 5). 3.(2.5 points) What is the probability that you have to play the game 4 times before you roll Z=7? 4. (2.5...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be X-Y). The range of Z will be from 0 to 3. 1. (2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 21Z >1). 3. (2.5 points) What is the probability that you have to play the game 6 times before you roll...
Fair diced, which is unbiased. Each throw is independent.
Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y], rounded to nearest .xx.
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X-Y). The range of Z will be from -3 to 3. 1. (2.5 points) Find E(Z). 2. (2.5 points) Find P(Z =-1|Z < 1). 3. (2.5 points) What is the probability that you have to play the game 3 times before you roll...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X-Y). The range of Z will be from -3 to 3. 1. (2.5 points) Find E(Z). 2. (2.5 points) Find P(Z =-1|Z < 1). 3. (2.5 points) What is the probability that you have to play the game 3 times before you roll...
Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C_1, C_2, and C_3. C_1 will land Heads with probability 1/3. C_2 will land Heads with probability 1/5. C_3 will land Heads with probability 1/4. You roll the die. If the die lands with a 1 face up, flip coin C_1 If the die...
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