Question 3 Suppose an unfair die is to an unfair die is rolled. Let random variable...
An unfair die was rolled 120 times. Below is a frequency table for the number of times it landed on each value: Number Frequency 1 27 2 39 3 21 4 18 5 6 6 9 Determine the probability that the die will land on a number less than 3 if it is going to be rolled again.
Suppose you have a die that has probability p of resulting in the outcome 6 when rolled, where p is a continuous random variable that is uniformly distributed over [O, j]. Suppose you start rolling this die. (The value of p does not change once you start rolling.) Give exact answers as simplified fractions. (a) Compute the probability that the first roll is 6. b) Compute the probability that the first two rolls are both 6. (c) Let Si be...
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
Exercise 5.11. Suppose a fair 1-sided die is rolled, and the random variable X (s) outputs - 1 if the roll is 2, and 1 if the roll is 1,3, or 1. Calculate Mx(2).
Numbers rolled on a Die Number on DieJulieSam Meghan 0 8 2 4 4 Julie, Sam, and Meghan are performing an experiment. They each rolled a die 20 times and the table shows their results. 1. What was the experimental probability that Meghan rolled a 5? 2. Based on her results, what is the theoretical probability that Julie will roll a 4 on her next roll? 3. One of the questions on the lab sheets asks them to determine the...
Suppose that a fair die is rolled n times. We say that there is an increase at the i’th place if result on the i + 1’st roll is greater than the result on the i’th roll. Let X be a random variable representing the number of increases. Find E[X].
This question is due my 11:50pm EST One die is rolled 2 times in a row. The observation is the number that comes up on each roll (rolling 2 and 5 is not the same as rolling 5 and 2). Describe one outcome and find a number of outcomes. Write all outcomes of the sample space S (you can use … notation to indicate many numbers of cases). : “pairs are rolled” (both dice come up the same number) Write...
a 6-sided die is rolled . The set of equally likely outcomes is {1,2,3,4,5,6}. Find the probability of rolling a number less than 10.
A coin is tossed and a six-sided die numbered 1 through 6 is rolled. Find the probability of tossing a head and then rolling a number greater than 2. The probability of tossing a head and then rolling a number greater than 2 is _______ (Round to three decimal places as needed.)
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil- ity of rolling the value i is Pi, i = 1, … ,6. Let Xn denote the number of distinct values that appear in n rolls. (a) Find E|X, and E21 (b) What is the probability that in the n rolls of the dice, for n 2 3, a 1, 2, and 3 are each rolled at least once?