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### Which of the following can be represented by a discrete random variable?

Which of the following can be represented by a discrete random variable?

Which of the following can be represented by a discrete random variable?

### Random Variables ^{[1]}

A random variable, usually written X, is a variable whose possible. values are numerical outcomes of a random phenomenon

a countable number of distinct values such as 0,1,2,3,4,……… Discrete random variables are usually (but not necessarily) counts.

the number of children in a family, the Friday night attendance at a. cinema, the number of patients in a doctor’s surgery, the number of

### Statistics for the Social Sciences ^{[2]}

– Distinguish between discrete random variables and continuous random variables.. In our previous discussion of probability distributions, we did not distinguish between probability distributions for categorical and quantitative variables

We looked at the probability distribution for the categorical variable blood type. We also looked at the probability distribution for the quantitative variable number of boreal owl eggs in a nest

These distributions will be very important when we study statistical inference. When the outcomes are quantitative, we call the variable a random variable

### Random Variables ^{[3]}

A random variable, usually written X, is a variable whose possible. values are numerical outcomes of a random phenomenon

a countable number of distinct values such as 0,1,2,3,4,……… Discrete random variables are usually (but not necessarily) counts.

the number of children in a family, the Friday night attendance at a. cinema, the number of patients in a doctor’s surgery, the number of

### Expert Maths Tutoring in the UK ^{[4]}

A discrete random variable is a variable that can take any whole number values as outcomes of a random experiment. The discrete random variable takes a countable number of possible outcomes and it can be counted as 0, 1, 2, 3, 4, ……

A discrete random variable is also known as a stochastic variable. Examples of a discrete random variable are a binomial random variable and a Poisson random variable.

Also, a discrete random variable should not be confused with an algebraic variable. An algebraic variable takes only one value, but a discrete random variable takes numerous values.

### Discrete Random Variables ^{[5]}

It is often the case that a number is naturally associated to the outcome of a random experiment: the number of boys in a three-child family, the number of defective light bulbs in a case of 100 bulbs, the length of time until the next customer arrives at the drive-through window at a bank. Such a number varies from trial to trial of the corresponding experiment, and does so in a way that cannot be predicted with certainty; hence, it is called a random variable

A random variableA numerical value generated by a random experiment. is a numerical quantity that is generated by a random experiment.

Table 4.1 “Four Random Variables” gives four examples of random variables. In the second example, the three dots indicates that every counting number is a possible value for X

### Discrete Random Variable: Meaning & Types ^{[6]}

Have you ever played an archery game and tried to see how many times you can throw an arrow before hitting a particular target? When you do this, you are testing the probabilities and outcomes of random events. We can express and describe the outcomes of random events with random variables.Discrete random variables are a type of random variable in…

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Have you ever played an archery game and tried to see how many times you can throw an arrow before hitting a particular target? When you do this, you are testing the probabilities and outcomes of random events. We can express and describe the outcomes of random events with random variables.

### Lesson Explainer: Discrete Random Variables ^{[7]}

In this explainer, we will learn how to identify a discrete random variable and define its corresponding probability distribution.. In order to understand what a discrete random variable is, it is helpful to discuss what a random variable is first.

As with probabilities of mutually exclusive events, the probabilities associated with all the values that the random variable can take must all add up to 1. Moreover, each probability must lie within the interval .

For a discrete random variable, the values of the random value must be discrete. Typically, they will take integer values, but this is not necessarily the case.

### Discrete and Continuous Random Variables ^{[8]}

A discrete variable is a variable whose value is obtained by counting.. A continuous variable is a variable whose value is obtained by measuring.

▪ A random variable is denoted with a capital letter. ▪ The probability distribution of a random variable X tells what the possible values of X are and how probabilities are assigned to those values

Then the probability distribution of X is as follows:. To graph the probability distribution of a discrete random variable, construct a probability histogram.

### Basic Concepts of Discrete Random Variables Solved Problems ^{[9]}

Let $X$ be a discrete random variable with the following PMF \begin{equation} \nonumber P_X(x) = \left\{ \begin{array}{l l} 0.1 & \quad \text{for } x=0.2\\ 0.2 & \quad \text{for } x=0.4\\ 0.2 & \quad \text{for } x=0.5\\ 0.3 & \quad \text{for } x=0.8\\ 0.2 & \quad \text{for } x=1\\ 0 & \quad \text{otherwise} \end{array} \right. – Find $R_X$, the range of the random variable $X$.

– The event $X\leq 0.5$ can happen only if $X$ is $0.2, 0.4,$ or $0.5$. $P(X\leq 0.5)$ $= P(X \in \{0.2, 0.4, 0.5\})$ $= P(X=0.2)+P(X=0.4)+P(X=0.5)$ $=P_X(0.2)+P_X(0.4)+P_X(0.5)$ $=0.1+0.2+0.2=0.5$

– This is a conditional probability problem, so we can use our famous formula. $P(X=0.2 | X

### Objective Question Answer for Discrete Random Variable Quiz ^{[10]}

Discrete Random Variable MCQ Quiz – Objective Question with Answer for Discrete Random Variable – Download Free PDF. Latest Discrete Random Variable MCQ Objective Questions

The mean and the standard deviation are respectively. Discrete Random Variable Question 1 Detailed Solution

\(Variance = \sum\limits_{i = 1}^4 {{p_i}} {({x_i} – E(x))^2}\). \(E(X) = \sum\limits_{i = 1}^4 {{p_i}} {x_i}\) = 0.1 × 1 + 0.2 × 2 + 0.3 × 3 + 0.4 × 4 = 3

### Sources

- http://www.stat.yale.edu/Courses/1997-98/101/ranvar.htm#:~:text=Examples%20of%20discrete%20random%20variables,in%20a%20box%20of%20ten.
- https://courses.lumenlearning.com/suny-hccc-wm-concepts-statistics/chapter/discrete-random-variables-1-of-5/#:~:text=Blood%20type%20is%20not%20a,also%20a%20continuous%20random%20variable.
- http://www.stat.yale.edu/Courses/1997-98/101/ranvar.htm
- https://www.cuemath.com/algebra/discrete-random-variable/
- https://saylordotorg.github.io/text_introductory-statistics/s08-discrete-random-variables.html
- https://www.studysmarter.co.uk/explanations/math/statistics/discrete-random-variable/
- https://www.nagwa.com/en/explainers/393149702678/
- http://www.henry.k12.ga.us/ugh/apstat/chapternotes/7supplement.html
- https://www.probabilitycourse.com/chapter3/3_1_6_solved3_1.php
- https://testbook.com/objective-questions/mcq-on-discrete-random-variable–5eea6a0a39140f30f369dd04