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What are the two requirements for a discrete probability distribution? Answer:Step 1 of 1Two Requirements for a Probability distributiona) Each probabilities must be between 0 and 1 b) The sum of the probabilities must be equal to 1. [The probability distribution of a discrete random variable X assigns a probability

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## Solution for problem 3AYU Chapter 6.1

Fundamentals of Statistics | 4th Edition

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What are the two requirements for a discrete probability distribution?

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Answer: Step 1 of 1

Two Requirements for a Probability distribution

a) Each probabilities must be between 0 and 1

b) The sum of the probabilities must be equal to 1.

[The probability distribution of a discrete random variable X assigns a probability to each possible values of the variable. Each probability is a number between 0 and 1, and the sum of the probabilities of all possible values equals 1.

Let xi , i = 1, 2, . . . , k, denote a possible outcome for the random variable X, and let P(X = xi) = P(xi) = pi denote the probability of that outcome.

Then 0 ≤ P(xi) ≤ 1 and P(xi) = 1 since each probability falls between 0 and 1, and since the total probability equals 1.]

Step 2 of 1

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### Textbook: Fundamentals of Statistics

### Edition: 4

### Author: Michael Sullivan,III

### ISBN: 9780321838704

Fundamentals of Statistics was written by and is associated to the ISBN: 9780321838704. This textbook survival guide was created for the textbook: Fundamentals of Statistics, edition: 4. Since the solution to 3AYU from 6.1 chapter was answered, more than 315 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 3AYU from chapter: 6.1 was answered by , our top Statistics solution expert on 04/03/17, 08:02AM. The answer to “What are the two requirements for a discrete probability distribution?” is broken down into a number of easy to follow steps, and 10 words. This full solution covers the following key subjects: ayu, Discrete, distribution, Probability, requirements. This expansive textbook survival guide covers 51 chapters, and 2146 solutions.

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## STATISTICS 125

STATISTICS 125 Learn with flashcards, games, and more — for free.

## STATISTICS 125 - CHAPTER 6.1 Discrete Random Variables

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What are the two requirements for a discrete probability distribution?

Click card to see definition 👆

The first rule states that the sum of the probabilities must equal 1. The second rule states that each probability must be between 0 and 1, inclusive.

Let P(x) = 1 1. ∑ P(x) = 1 2. 0 ≤ P(x) ≤

Click again to see term 👆

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

(a) The number of points scored during a basketball game.

(b) The time it takes to fly from City Upper A to City Upper B.

Click card to see definition 👆

(a) The random variable is discrete. The possible values are x = 0, 1, 2,....

(b) The random variable is continuous. The possible values are t > 0.

Click again to see term 👆

1/6 Created by mmontesd STATISTICS 125

### Terms in this set (6)

What are the two requirements for a discrete probability distribution?

The first rule states that the sum of the probabilities must equal 1. The second rule states that each probability must be between 0 and 1, inclusive.

Let P(x) = 1 1. ∑ P(x) = 1 2. 0 ≤ P(x) ≤

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

(a) The number of points scored during a basketball game.

(b) The time it takes to fly from City Upper A to City Upper B.

(a) The random variable is discrete. The possible values are x = 0, 1, 2,....

(b) The random variable is continuous. The possible values are t > 0.

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

(a) The number of people in a restaurant that has a capacity of 300.

(b) The distance a baseball travels in the air after being hit.

(a) The random variable is discrete. The possible values are x=0, 1, 2,...comma 300.

(b)The random variable is continuous. The possible values are d > 0.

Is the distribution a discrete probability distribution?

x P(x) 0 0.07 1 0.34 2 0.27 3 0.15 4 0.17

Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive.

Determine the required value of the missing probability to make the distribution a discrete probability distribution.

x P(x) 3 0.34 4 ? 5 0.08 6 0.29

In a discrete probability distribution, the sum of the probabilities must equal 1, and all probabilities must be greater than or equal to 0 and less than or equal to 1.

Notice that all the given probabilities are greater than or equal to 0 and less than or equal to 1.

The probability P(4) is missing from the distribution. To find P(4), first add all of the given probabilities.

∑ P(4) = 0.34 + 0.08 + 0.29 = 0.71

Recall that the sum of all the probabilities must equal 1 in a discrete probability distribution. To find P(4), subtract the sum of the other probabilities from 1.

1.00 - 0.71 = 0.29

The value for P(4) is a valid probability because it is greater than or equal to 0 and less than or equal to 1.

Thus, P(4)=0.29 makes the probability distribution valid.

In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Complete parts (a) through (f) below.

x P(x) 0 0.263 1 0.576 2 0.127 3 0.029 4 0.004 5 0.001

(a) Verify that this is a discrete probability distribution.

In a discrete probability distribution, all of the probabilities are between 0 and 1, inclusive, and the sum of the probabilities is 1.

Identify the smallest probability in this distribution.

The smallest probability is 0.001.

Identify the greatest probability in this distribution.

The greatest probability is 0.576.

So all of the probabilities are between 0 and 1, inclusive. Now find the sum of the probabilities.

0.263+0.576+0.127+0.029+0.004+0.001=1

So the sum of the probabilities is 1. This verifies that this is a discrete probability distribution.

(b) Draw the graph of the discrete probability distribution. Describe the shape of the distribution.

The distribution has one mode and is skewed right.

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## What are the two requirements for the probability distributions of discrete random variables?

In the development of the probability function for a discrete random variable, two conditions must be satisfied: (1) f(x) must be nonnegative for each value of the random variable, and (2) the sum of the probabilities for each value of the random variable must equal one.

## What are the two requirements for the probability distributions of discrete random variables?

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In the development of the **probability** function for a **discrete random variable**, **two** conditions must be satisfied: (1) f(x) must be nonnegative for each value of the **random variable**, and (2) the sum of the **probabilities** for each value of the **random variable** must equal one.

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Furthermore, what are the 2 requirements for a discrete probability distribution?

**A probability experiment that has the following conditions:**

Each trial can have only two outcomes or outcomes that can be reduced to two. outcomes.

There must be a fixed number of trials.

The outcomes of each trial must be independent of each other.

The probability of success must remain the same for each trial.

Additionally, how do you create a probability distribution of a discrete random variable? A **discrete random variable** has a countable number of possible values. The **probability** of each value of a **discrete random variable** is between 0 and 1, and the sum of all the **probabilities** is equal to 1. A continuous **random variable** takes on all the values in some interval of numbers.

Also know, what is a probability distribution for a discrete random variable?

The **probability distribution**. of a **discrete random variable** X is a list of each possible value of X together with the **probability** that X takes that value in one trial of the experiment. Each **probability** P(x) must be between 0 and 1: 0≤P(x)≤1. The sum of all the **probabilities** is 1: ΣP(x)=1.

How do you calculate the mean of a discrete random variable?

Use the following formula to **compute the mean of a discrete random variable**. where xi is the value of the **random variable** for outcome i, μx is the **mean** of **random variable** X, and P(xi) is the probability that the **random variable** will be outcome i.

**Example**1.

Number of hits, x Probability, P(x)

0 0.10 1 0.20 2 0.30 3 0.25

35 Related Question Answers Found

### What are the laws for a discrete probability density function?

For **discrete probability** ∑i pi = 1, where the sum is over all possible outcomes. About Rule 1: pi = 0 implies that the given outcome never happens, whereas pi = 1 implies that this outcome is the only possibility (and always happens). Any value inside the range (0,1) means that the outcome occurs some of the time.

### What makes a discrete probability distribution valid?

To be a **valid discrete probability distribution**, we need: the sum of the **probabilities** of all the possible values of the random variable to be 1, i.e., X Pr ( X = x ) = 1 ; the **probabilities** of each possible value of the random variable to lie between 0 and 1, i.e., 0 ≤ Pr ( X = x ) ≤ 1 .

### What are the two criteria for a valid probability distribution?

b) Discrete **Probability distribution** consists of the values a random variable can assume and the corresponding **probabilities** of the values. a) All **probabilities** must between 0 and 1 b) The sum of the **probabilities** must add up to 1. Continuous RANDOM VARIABLE – The number of values that X can assume is INFINITE.

### How do you find the probability distribution?

**How to find the mean of the probability distribution: Steps**

Step 1: Convert all the percentages to decimal probabilities. For example:

Step 2: Construct a probability distribution table.

Step 3: Multiply the values in each column.

Step 4: Add the results from step 3 together.

### What is a proper probability distribution?

A **probability** function is a function which assigns **probabilities** to the values of a random variable. All the **probabilities** must be between 0 and 1 inclusive. The sum of the **probabilities** of the outcomes must be 1.

### What is an example of a discrete random variable?

A **discrete variable** is a **variable** which can only take a countable number of values. In this **example**, the number of heads can only take 4 values (0, 1, 2, 3) and so the **variable** is **discrete**. The **variable** is said to be **random** if the sum of the probabilities is one. Probability Density Function.

### What are the different probability distributions?

There are many **different** classifications of **probability distributions**. Some of them include the normal **distribution**, chi square **distribution**, binomial **distribution**, and Poisson **distribution**. A binomial **distribution** is discrete, as opposed to continuous, since only 1 or 0 is a valid response.

### What makes a discrete probability distribution?

A **discrete distribution** describes the **probability** of occurrence of each value of a **discrete** random variable. A **discrete** random variable is a random variable that has countable values, such as a list of non-negative integers. Thus, a **discrete probability distribution** is often presented in tabular form.

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