dice is unbiased. Throws independent.
dice is unbiased. Throws independent. Step 1. You roll a six-sided die. Let X be the...
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.
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.
Roll two fair four-sided dice. Let X and Y be the die scores from the 1st die and the 2nd die, respectively, and define a random variable Z = X − Y (a) Find the pmf of Z. (b) Draw the histogram of the pmf of Z. (c) Find P{Z < 0}. (d) Are the events {Z < 0} and {Z is odd} independent? Why?
The final answer is 4.472
2. You roll two fair, six-sided dice. Let X be the number on the first die. Let Y be the number on the second die. Calculate E[max(X,Y)], the expected value of the larger of the two numbers. There are several ways you can do this. You should try to do this by applying 2D LOTUS to the joint distribution of X and Y , which is extremely simple. To check your answer, you can use...
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 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...
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...