Create fair die – Can you make a fair die? Make a two cubes out of...

Create fair die – Can you make a fair die? Make a two cubes out of paper or clay. Label the faces 1 - 6 (or whatever). Toss your cube 100 times, and keep a tally of the results. Run a Chi-square Goodness of Fit Test to see if you have evidence to say your cube unfair. Submit a one page write up with data, calculations and conclusion. Since we have not discussed this test, you can earn extra credit for this project if done correctly.

Expert Solution

orchestra answered 2 years ago

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are...

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. a) Distinguish between the outcomes and events. b) What is the probability that both die roll ones? c) What is the probability that exactly one die rolls a one? d) What is the probability that neither die rolls a one? e) What is the expected number of ones? f) If you did this 1000 times, approximately...

You are to make a bowling ball out of 2024-0 by forging in an impression die...

You are to make a bowling ball out of 2024-0 by forging in an impression die with flash. What force (tons) is needed? What will be the weight of the finished bowling ball? Yield strength = 75 MPa = 11 ksi Ultimate tensile strength = 190 MPa = 27 ksi Max bowling ball diameter = 8.595 inches Density = 0.1 lbs/in3

A fair red die and a fair green die are rolled. (a) What is the probability...

A fair red die and a fair green die are rolled. (a) What is the probability that the sum of the numbers is even? (b) What is the probability that the number on the red die is more than the number on the green die? (c) What is the probability that the number on the red die is twice the number on the green die? (d) What is the probability that the number on the red die is different from...

Question Manufacturers are testing a die to make sure that it is fair (has a uniform...

Question Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 84 times and record the outcomes in the table below. Outcome 1 2 3 4 5 6 Expected 14 14 14 14 14 14 Observed 17 12 15 5 16 19 They perform a chi-square Goodness-of-Fit Test. The first few steps are summarized below. H0: The die is fair. Ha: The die is not fair. α=0.01 The test statistic,...

Two fair coins and a fair die are tossed. Find the sample space of the experiment...

Two fair coins and a fair die are tossed. Find the sample space of the experiment (10 pts); Find the probabilities of the following events: A- ”the die shows 2 or 3” (5 pts); B- ”one of the coins is head, the other - tail, and the die shows an odd number” (5 pts). Are the events A and B independent? (5 pts). Give proofs.

Two rolls of a fair die. Let x and y be the results of the two...

Two rolls of a fair die. Let x and y be the results of the two rolls, and let z = x + y. (a) Find P[x = 4, y = 3], P[x > 3, y = 5]. (b) Find P[z = 7], P[z = 5], P[z = 3]. (c) Find the probability that at least one 6 appears given that z = 8. (d) Find the probability that x = 6 given that z > 8. (e) Find the...

Consider an experiment where fair die is rolled and two fair coins are flipped. Define random...

Consider an experiment where fair die is rolled and two fair coins are flipped. Define random variable X as the number shown on the die, minus the number of heads shown by the coins. Assume that all dice and coins are independent. (a) Determine f(x), the probability mass function of X (b) Determine F(x), the cumulative distribution function of X (write it as a function and draw its plot) (c) Compute E[X] and V[X]

Five fair die are rolled. What is the probability of at most two of the dice...

Five fair die are rolled. What is the probability of at most two of the dice coming up a one or a six? Your workings should show the use of appropriate laws and formulae — do not provide a purely arithmetic answer.

You have two 5-sided fair dice. If you roll any individual die, the possible results are...

You have two 5-sided fair dice. If you roll any individual die, the possible results are 1, 2, 3, 4, or 5 each equally likely. Let A1 be the random result on the first die, and A2 be the random result on the second die. We define the random variable A = A1 + A2, the sum of values of two dice. Assume the signal X(t) = A for all times t. (a) Is A a discrete or a continuous...

stat question and please explain, thank you A fair die is tossed two times independently: let...

stat question and please explain, thank you A fair die is tossed two times independently: let W denote the product of the outcomes. Find the probability that W = 6.

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