5. Consider the probability experiment is for you to roll a 9-sided die and a 4-sided...
Consider a fair six-sided die. (a) What is its probability mass function? Graph it. It represents the population distribution of outcomes of rolls of a six-sided die (b) How would you describe the population distribution? (c) What is the sampling distribution of x for a six-sided fair die, when its rolled 100 times? Describe it with as much specificity as possible. NOTE: Roll of a die is a discrete variable. Why is it ok to use the Normal distribution to...
7. Pairwise Independence. Roll a red 4-sided die and a white 4-sided die. A: the red die is even B: the white die is even C: the sum of the two dice is even a) Show that A, B, and C are pairwise independent. b) Show that A n B and C are NOT independent. 8. Roll a red 6-sided die and a white 6-sided die. D: red die is 1 or 2 or 3 Show that P(D กั E...
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $12. If you roll a 4 or 5, you win $1. Otherwise, you pay $2. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table х P(X) b. Find the expected profit. $ (Round to the nearest cent)
An experiment is performed where a 4-sided die is rolled and then another 4-sided die is rolled. The possible outcomes for both events are 1, 2, 3, and 4. Identify the sample space for this experiment.
i. Consider a weighted 6-sided biased die that is twice as likely to produce any even outcome as any odd outcome. What is the expected value of 1 roll of this die? What is the expected value of the sum of 9 rolls of this die? ii. Let X denote the value of the sum of 10 rolls of an unweighted 6-sided die. What is Pr(X = 0 mod 6)? (Hint: it is sufficient to consider just the last roll)...
Suppose you roll a special 39-sided die. What is the probability that one of the following numbers is rolled? 17 39 35 Probability = ______(Round to 4 decimal places)
There exists 3-sided dice. Such a die, when you roll it, will show 1, 2, or 3 with equal probability. The experiment is to roll 3 such dice. Random variable T is the total of all 3 dice. t P(T=t) 3 4 5 6 7 8 9
i. Consider a weighted 6-sided die that is twice as likely to produce any even outcome as any odd outcome. What is the expected value of 1 roll of this die? What is the expected value of the sum of 9 rolls of this die? ii. Let X denote the value of the sum of 10 rolls of an unweighted 6-sided die. What is Pr(X = 0 mod 6)? (Hint: it is sufficient to consider just the last roll) *side...
Consider that an 10-sided die, numbered 1-10, is rolled. Find the probability that the roll results in an odd number or a number greater than nine? a) 0.70 b) 0.80 Oc) 0.60 d) 0.85 O e) 0.90
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...