4. Suppose you roll a fair die. Then S {1,2,3,4,5,6}. Let X(3) = \3/2] where 13/2]...

Question

Question

$4. Suppose you roll a fair die. Then S {1,2,3,4,5,6}. Let X(3) = \3/2] where 13/2] is the greatest integer less than or equal$

math Statistics-And-Probability

Answer 1

Answer #1

a. P({X = 0}) = P({1}) = 6. P({X € {0,1}}) = P({1,2}) c. P({X<2})= P({1,2,3,4}) d. P({X = 1.5}) = P({3}) = = OLAN CONCO

Answer 2

Similar Homework Help Questions

Problem 2 (5 points) Roll a fair die 5 times. Let X denote the number of...

Problem 2 (5 points) Roll a fair die 5 times. Let X denote the number of sixes that appear. • What is yux? • What is ox?
Roll two fair four-sided dice. Let X and Y be the die scores from the 1st...

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?
Please show work :) Will upvote/rate! 3. Discrete Random Variables You have a biased die, where the probability that a...

Please show work :) Will upvote/rate! 3. Discrete Random Variables You have a biased die, where the probability that a number n appears on the die when it is rolled is defined as a random variable X such that Р(X %3D п) — с:п Here c is a positive real number. Now answer the questions below: (a) Find the value of c (b) What is the expected value of the random variable X? (c) Find how close a number you...

problem 4 you repeatedly roll an ordinary eight-sided die five times. Let X equal the number...

problem 4 you repeatedly roll an ordinary eight-sided die five times. Let X equal the number of times you roll the die. Let Y equal the value of the first roll What is E[x] and E[Y]
Fair diced, which is unbiased. Each throw is independent. Step 1. You roll a six-sided die....

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.
2. Let X denote the outcome the outcome of a die roll. (i) Compute E[X] given...

2. Let X denote the outcome the outcome of a die roll. (i) Compute E[X] given that the roll is fair; (ii) construct a distribution function for X such that for all a (3.5,6)., E[x] a

4. We want to test whether a die is fair. We roll it 300 times and...

4. We want to test whether a die is fair. We roll it 300 times and records the outcomes as meaning we rolled a 1 on the die 54 times, etc. (a) A fair die has probability 1/6 for each of the six outcomes. Use a chi-squared test to test whether or not the probabilities are all equal. (b) An oblong die will have P(1) = P(6), P(2) = P(5) and P(3) = P(4), but all of the probabilities will...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...

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...
You roll a pair of fair 6-sided dice: a red die and a blue die. (a)...

You roll a pair of fair 6-sided dice: a red die and a blue die. (a) Consider event A: {the outcome of the red die is more than 3} and event B: {the outcome of the red die is less than 5}. Given that event A occurs, what is the probability that event B occurs? (b) Are A and B mutually exclusive (i.e., disjoint)? (c) Are A and B independent? (d) Calculate the probability of event C: {the outcome of...

You roll a pair of fair 6-sided dice: a red die and a blue die. (a)...

You roll a pair of fair 6-sided dice: a red die and a blue die. (a) Consider event A: {the outcome of the red die is more than 3} and event B: {the outcome of the red die is less than 5}. Given that event A occurs, what is the probability that event B occurs? (b) Are A and B mutually exclusive (i.e., disjoint)? (c) Are A and B independent? (d) Calculate the probability of event C: {the outcome of...