Question

In: Statistics and Probability

Two 6-sided dice are rolled. One die is a standard die, and the other is a...

Two 6-sided dice are rolled. One die is a standard die, and the other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8.

a. What is the probability distribution of this experiment?

b. What is the shape of the probability distribution?

c. What is the expected value when these 2 dice are rolled?

Expert Solution

a)

The outcome (sum) of the roll of two die,

		Fabonacci die
		1	1	2	3	5	8
Standard die	1	2	2	3	4	6	9
	2	3	3	4	5	7	10
	3	4	4	5	6	8	11
	4	5	5	6	7	9	12
	5	6	6	7	8	10	13
	6	7	7	8	9	11	14

The probability distribution of this experiment is,

Sum	2	3	4	5	6	7	8	9	10	11	12	13	14
Prob	2/36	3/36	4/36	4/36	5/36	5/36	3/36	3/36	2/36	2/36	1/36	1/36	1/36

b)

The frequency distribution of this experiment is,

Sum	Frequency
2	2
3	3
4	4
5	4
6	5
7	5
8	3
9	3
10	2
11	2
12	1
13	1
14	1

The column plot (histogram) for this frequency is shown below,

The frequency distribution is normally distributed with slightly right tailed distribution.

c)

The expected value is obtained using the formula,

Sum, X	2	3	4	5	6	7	8	9	10	11	12	13	14
Prob, P(X)	2/36	3/36	4/36	4/36	5/36	5/36	3/36	3/36	2/36	2/36	1/36	1/36	1/36

Sum, X	2	3	4	5	6	7	8	9	10	11	12	13	14
Prob, P(X)	0.06	0.08	0.11	0.11	0.14	0.14	0.08	0.08	0.06	0.06	0.03	0.03	0.03
X*P(X)	0.111	0.25	0.444	0.556	0.833	0.972	0.667	0.75	0.556	0.611	0.333	0.361	0.389

orchestra answered 1 year ago

Part 1: Two 6-sided dice are rolled. One die is a standard die, and the other...

Part 1: Two 6-sided dice are rolled. One die is a standard die, and the other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8. Submit a file with the probability distribution for this experiment. Part 2: Two 6-sided dice are rolled. One die is a standard die, and the other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8. What is the shape of the probability distribution? Part 3: Two 6-sided...

One red (6 sided) and one white (6 sided) dice is rolled. The random variable X...

One red (6 sided) and one white (6 sided) dice is rolled. The random variable X has the value 1 if the red dice shows a number max 2 and is 2 else. The random variable y has the value 1 if the white dice shows a uneven number and is 2 else. A) determine the common probability function (x, y) B) determine the marginal probability functions of x and y C) calculate e(x), e(x^2), var(x), e(y), e(y^2), and var(y)

Consider rolling two four sided dice. One die is blue and the other is green. (a)...

Consider rolling two four sided dice. One die is blue and the other is green. (a) State the sample space. (b) Compute the probability of getting two even numbers. (c) Compute the probability of getting an even sum if the blue die rolls a 2. What is the probability of drawing a four or a heart when drawing a single card from a standard deck of cards.

If a fair coin is flipped twice and a standard 6 sided die is rolled once,...

If a fair coin is flipped twice and a standard 6 sided die is rolled once, what is the likelihood of getting two 'heads' on the coin and a '1' on the die? â€‹Express your answer as a percent rounded to the tenth place

Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting...

Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting sum less than or equal to 5 for the first time on the 4th roll? Show your work to receive credit.

Two 6-sided dice are rolled. Let X be the larger of the two numbers showing. For...

Two 6-sided dice are rolled. Let X be the larger of the two numbers showing. For each i from 1 to 6, find the probability that X = i.

(5) A fair 6-sided dice is rolled twice. The fairness of the dice consists of the...

(5) A fair 6-sided dice is rolled twice. The fairness of the dice consists of the following facts: (i) no face of the dice is likelier to be rolled than any other (so a roll of a 5 and a roll of a 3 are equiprobable) and (ii) the dice has no “memory” - each roll is independent of any other. 5.1: What is the probability that you’ve first rolled a 3 and the pair of rolls sums to something...

A fair six-sided die is rolled repeatedly until the third time a 6 is rolled. Let...

A fair six-sided die is rolled repeatedly until the third time a 6 is rolled. Let X denote the number of rolls required until the third 6 is rolled. Find the probability that fewer than 5 rolls will be required to roll a 6 three times.

Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled....

Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled. Let - X1 be the random variable which is 1 if the numbers rolled on the blue die and the yellow die are the same and 0 otherwise; - X2 be the random variable which is 1 if the numbers rolled on the red die and the yellow die are the same and 0 otherwise; - X3 be the random variable which is 1...

Two dice are rolled one after the other. Find the probability that the sum of the...

Two dice are rolled one after the other. Find the probability that the sum of the dots on the dice total is a number greater than 11 if the second die is a 5.