Part A: Theoretically, if you roll two six sided
dice and variable x is the total of the two outcomes, the possible
values that x can take are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and
12.
Write the probability distribution of x. ( Chapter 5)
Calculate mean, variance and standard deviation of x. ( Chapter
5)
Part A: Theoretically, if you roll two six sided dice and variable x is the total...
You roll a pair of standard six–sided dice and record the largest of the two outcomes. Let X be random variable associated with the outcome of this experiment. (b) What is the probability mass function (PMF) of X? (c) What is the cumulative distribution function (CDF) of X?
Consider three six-sided dice, and let random variable Y = the value of the face for each. The probability mass of function of Y is given by the following table: y 1 2 3 4 5 6 otherwise P(Y=y) 0.35 0.30 0.25 0.05 0.03 0.02 0 Roll the three dice and let random variable X = sum of the three faces. Repeat this experiment 50000 times. Find the simulated probability mass function (pmf) of random variable X. Find the simulated...
Write a Code in Java or Python, for the following scenario(s): Consider three six-sided dice, and let random variable Y = the value of the face for each. The probability mass of function of Y is given by the following table: y 1 2 3 4 5 6 otherwise P(Y=y) 0.35 0.30 0.25 0.05 0.03 0.02 0 Roll the three dice and let random variable X = sum of the three faces. Repeat this experiment 50000 times. Find the simulated...
4. You roll a fair six-sided dice twice and record the results, in order. The sample space is 2,6 6,6) (a) How many possible outcomes are there? (b) What is the probability that the total (sum) of the results is equal to 10? (c) Given that the total is equal to 10, what is the probability that the first roll was a 4? (d) Given that the first roll was not a 4, what is the probability that the total...
For the two six-sided dice case: Write out the six-by-six matrix showing all possible (36) combinations of outcomes. Draw a histogram of the probability of outcomes for the dice totals. Explain the shape of the histogram. Draw a Venn diagram for the 36 dice roll combinations. Define a set "A" as all the combinations that total seven; define set "B" as all the combinations that have one die roll (either die 1 or 2) equal to 2. Indicate the sets...
If you roll two six-sided dice, what is the probability of obtaining the following outcomes? a)2 or 3 b) 6 and 4 c) At least one 5 d) Two of the same number (two 1s, or two 2s, or two 3s, etc.) e) An even number on both dice f) An even number on at least one die and please show how you got the answers ex. P(something) = (1/2)*(1/3) = (1/6)
If you roll two six-sided dice, what is the probability of obtaining the following outcomes? a)2 or 3 b) 6 and 4 c) At least one 5 d) Two of the same number (two 1s, or two 2s, or two 3s, etc.) e) An even number on both dice f) An even number on at least one die and please show how you got the answers ex. P(something) = (1/2)*(1/3) = (1/6)
A) Suppose I roll two fair six-sided dice. What is the probability that I rolled a total of 5? B) Suppose I roll two fair six-sided die and I announce that the sum of the two die is 6 or less. What is the probability that I rolled a total of 5?
If you roll two fair six-sided dice, what is the probability that the sum is 4 or higher?
(A) If you roll 3 six-sided dice, what is the probability of getting an overall score of 8? (B) If you roll 3 six-sided dice 4 times, what is the probability of getting an overall score of 8 four times in a row? (C) If you roll 3 six-sided dice 2 times, what is the probability of getting an overall score of 8 on the first roll and an overall score of 3 on the second roll?