8. Suppose that two 6-sided dice are rolled. Let a random variable take on the value of an even sum. Hink this will be a conditional distribution.a.) Find the probability distribution.b.) Find the mean of the probability distribution.c.) Find the variance and the standard deviation of the probability distribution. Discrete Probability Distributions:8. Suppose that two 6-sided dice are rolled. Let a random variable take on the value of an even sum. Hint: thiswill be a conditional distribution.a.) Find the probability distribution.b.) Find the mean of the probability distribution.c.) Find the variance and the standard deviation of the probability distribution.

Answered: Discrete Probability Distributions: 8.…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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8. Suppose that two 6-sided dice are rolled. Let a random variable take on the value of an even sum. Hink this will be a conditional distribution. a.) Find the probability distribution. b.) Find the mean of the probability distribution. c.) Find the variance and the standard deviation of the probability distribution.

Discrete Probability Distributions:
8. Suppose that two 6-sided dice are rolled. Let a random variable take on the value of an even sum. Hint: this
will be a conditional distribution.
a.) Find the probability distribution.
b.) Find the mean of the probability distribution.
c.) Find the variance and the standard deviation of the probability distribution.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1: part a>

To solve this problem, we first need to list all the possible outcomes when rolling two 6-sided dice. Each die has 6 faces, so there are $6 cross times 6 equals 36$ total outcomes.

The outcomes with an even sum (2, 4, 6, 8, 10, or 12) can occur in the following ways:

1 way to get a sum of 2: (1, 1)
3 ways to get a sum of 4: (1, 3), (2, 2), (3, 1)
5 ways to get a sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
5 ways to get a sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
3 ways to get a sum of 10: (4, 6), (5, 5), (6, 4)
1 way to get a sum of 12: (6, 6)

Now, let's calculate the probabilities for each of these outcomes:

a.) Probability Distribution:

P(sum = 2) = 1/36
P(sum = 4) = 3/36 = 1/12
P(sum = 6) = 5/36
P(sum = 8) = 5/36
P(sum = 10) = 3/36 = 1/12
P(sum = 12) = 1/36

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