> set.seed(10)
> library(purrr)
> X = rdunif(1,6,1)
> s = 0
> for(i in 1:100)
+ {
+ y = sum(rdunif(X,6,1))
+ s = s + y
+ }
> Ey = s/100
> Ey
[1] 14.09
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Step 1. You roll a six-sided die. Let X be the (random) number that you obtain....
dice is unbiased. Throws 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.
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.
you repeatedly roll an ordinary six sided die five times. Let X equal the number of times you roll the die. For example (1,1,2,3,4) then x =4 Find E[X]
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...
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 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...
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 -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...