Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, Python, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

Best MCQs Random Variable Quiz 3

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The post is about Random Variable Quiz. There are 20 multiple-choice questions covering topics related to the basics of random variables, types of random variables, dependent and independent random variables, distribution of random variables, and mean and variance of random variables. Let us start with MCQs Random Variable Quiz.

Online MCQs about Random Variables with Answers

1. $Var(3X – 4Y)=$?

 
 
 
 

2. $Var(X/3)=$?

 
 
 
 

3. If $SD(X) = 3$ then $SD(X+4/6)$ is

 
 
 
 

4. If $X$ follows t-distribution with $v$ degrees of freedom then the distribution of $x^2$ is

 
 
 
 

5. A continuous random variable is a random variable that can

 
 
 
 

6. If $X$ is a random varaible, then $Var(2-3X)$ is

 
 
 
 

7. If $X$ is a random variables, $a$ and $b$ are constants then $E(aX+b)$ is equal to

 
 
 
 

8. If $Var(X) = 4$ then $Var(3X+5)$ is equal to

 
 
 
 

9. If $X$ is a continuous random variable, then function $f(x)$ is

 
 
 
 

10. $Var(2X+5) =$ ?

 
 
 
 

11. The distribution function $F(x)$ is equal to

 
 
 
 

12. If $X\sim N(\mu, \sigma^2)$ where $a$ and $b$ are real numbers, then variance of $(aX+b)$ is

 
 
 
 

13. For a continuous random variable, the area under the probability distribution curve between any two points is always

 
 
 
 

14. If $X$ and $Y$ are independent then $Var(X-Y)$ is

 
 
 
 

15. The probability that a continuous random variable assumes a single value is

 
 
 
 

16. If $X$ and $Y$ are independent random variables then $E(XY)$ is equal to

 
 
 
 

17. If $X$ and $Y$ are independent random variables then $VAR(X-Y)$ is equal to

 
 
 
 

18. For a normal distribution, the $Z$ value for an $X$ value is to the right of the mean is always

 
 
 
 

19. For a continuous random variable $X$, the total probability of the mutually exclusive events (intervals) within which $X$ can assume a value is

 
 
 
 

20. $Var(X+4)=$?

 
 
 
 

MCQs Random Variable Quiz

MCQs Random Variable Quiz with Answers
  • If $X$ and $Y$ are independent random variables then $E(XY)$ is equal to
  • If $X$ and $Y$ are independent random variables then $VAR(X-Y)$ is equal to
  • If $X$ is a random variables, $a$ and $b$ are constants then $E(aX+b)$ is equal to
  • If $X$ is a random varaible, then $Var(2-3X)$ is
  • $Var(2X+5) =$ ?
  • $Var(X+4)=$?
  • $Var(X/3)=$?
  • If $Var(X) = 4$ then $Var(3X+5)$ is equal to
  • If $SD(X) = 3$ then $SD(X+4/6)$ is
  • If $X$ and $Y$ are independent then $Var(X-Y)$ is
  • $Var(3X – 4Y)=$?
  • A continuous random variable is a random variable that can
  • For a continuous random variable, the area under the probability distribution curve between any two points is always
  • The probability that a continuous random variable assumes a single value is
  • For a continuous random variable $X$, the total probability of the mutually exclusive events (intervals) within which $X$ can assume a value is
  • If $X\sim N(\mu, \sigma^2)$ where $a$ and $b$ are real numbers, then variance of $(aX+b)$ is
  • For a normal distribution, the $Z$ value for an $X$ value is to the right of the mean is always
  • If $X$ follows t-distribution with $v$ degrees of freedom then the distribution of $x^2$ is
  • The distribution function $F(x)$ is equal to
  • If $X$ is a continuous random variable, then function $f(x)$ is
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Important Random Variable MCQ 2

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The post is about the Random Variable MCQ Test. There are 20 multiple-choice questions about random variables. The quiz covers topics related to the basic concept of random variables, real-life examples of random variables, random experiments, types of random variables, and distribution of random variables. Let us start the quiz random variable MCQ Test.

Please go to Important Random Variable MCQ 2 to view the test

Online Random Variable MCQ Test

Online Random Variable MCQs with Answers
  • A random variable is also called
  • A random variable assuming only a finite number of values is called:
  • A random variable assuming an infinite number of values is called
  • The number of students in a class is an example of
  • The speed of the car is an example of
  • Random numbers can be generated mechanically by
  • Suppose, four coins are tossed, the value of a random variable $H$ (No. of heads) is:
  • A quantity which can vary from one individual to another is called
  • A variable which can assume each and every value within a given range is called
  • The lifetime of a car tire is
  • Height measurements of 50 students studying in a college
  • A variable whose value is determined by the outcome of a random experiment is called
  • If $x$ is a discrete random variable, the function $f(x)$ is
  • If $X$ and $Y$ are random variables then $E(X+Y)$ is equal to
  • The sum of probabilities of a discrete random variable is
  • A chi-square random variable can assume the value:
  • The observed value of a statistic is:
  • If $X$ is a uniform variate $U(5, 10)$ then the mean of $X$ is
  • If $X$ is a uniform variate $U(5, 10)$ then the variance of $X$ is
  • If $X\sim N(\mu, \sigma^2)$ and $a$ and $b$ are real numbers, then the mean of $(aX+b)$ is
Random Variable MCQ Test

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Quartiles

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Introduction to Quantiles and Quartiles

Quantiles are the techniques used to divide the data into different equal parts. For example, quantiles divide the data into four equal parts. Quartile comes from quarter which means 4th part. Deciles divide the data into ten equal parts and they come from deca means the 10th part. Percentiles divide the data into hundred parts and it comes to percent which means the 100th part.

Therefore, quartiles, deciles, and percentiles are used to divide the data into 4, 10, and 100 parts respectively. The quantiles, deciles, and percentiles are collectively called quantiles.

Quartiles

Quartiles are the rules that divide the data into four equal parts. When we divide any data into four equal parts, we cut it at equidistant points. The quartiles ($Q_1, Q_2$, and $Q_3$) divide the data into four equal parts, so divide the number of observations by four for each quartile.

Quartiles for Ungroup Data

\begin{align*}
Q_1 &= \left(\frac{n+1}{4}\right)th \text{ value is the} \frac{1}{4} \text{ part}\\
Q_2 &= \left(\frac{2(n+1)}{4}\right)th \text{ value is the} \frac{2}{4} \text{ part}\\
Q_3 &=\left(\frac{3(n+1)}{4}\right)th \text{ value is the} \frac{3}{4} \text{ part}
\end{align*}

The following ungroup data has 96 observations $(n=96)$

222225253030303131333639
404042424848505152555759
818689899091919192939393
939494949596969697979898
999999100100100101101102102102102
102103103104104104105106106106107108
108108109109109110111112112113113113
113114115116116117117117118118119121

The first, second, and third quartiles of the above data set are:

\begin{align*}
Q_1 &= \left(\frac{n}{4}\right)th \text{ position } = \left(\frac{96}{4} = 24\right)th \text{ value} = 59\\
Q_2 &= \left(\frac{2\times 96}{4}\right) = 48th \text{ position} = 98\\
Q_3 &= \left(\frac{3\times n}{4}\right)th = \left(\frac{3\times 96}{}\right)th \text{ position} = 72th \text{ position} = 108
\end{align*}

Note that the above data is already sorted. If the data is not sorted, we first need to arrange/sort it in ascending order.

Quartiles for Gruoped Data

One can also compute the quantiles for the following grouped data, hence the quartiles.

ClassesfxC.B.CF
65-84974.564.5-84.59
85-1041094.584.5-104.519
105-12417114.5104.4.5-124.536
125-14410134.5124.5-144.546
145-1645154.5144.5-164.551
165-1844174.5164.5-184.455
185-2045194.5184.5-204.560
Total60   

From the above-grouped data, we have 60 observations $(n=60)= \sum\limits_{i=1}^n = f_i = \Sigma f = 60$. The three quartile will be

\begin{align*}
\frac{n}{4} &= \left(\frac{60}{4}\right)th = 15th \text{ value}\\
Q_1 &= l + \frac{h}{f}\left(\frac{n}{4} – CF\right) = 84.5 + \frac{20}{10}(15-9) = 96.5\\
\frac{2n}{4} &= \left(\frac{2\times 60}{4} \right) = 30th \text{ value}\\
Q_2 &= l + \frac{h}{f}\left(\frac{2n}{4} – CF\right) = 104.5 + \frac{20}{17}(30-19) = 117.44\\
\frac{3n}{4} &= \left(\frac{3\times 60}{4} \right) = 45th \text{ value}\\
Q_3 &= l + \frac{h}{f}\left(\frac{3n}{4} – CF\right) = 124.5 + \frac{20}{17}(45-36) = 142.5\\
\end{align*}

Frequently Asked Questions about Quantiles

  1. Define Quartiles, Deciles, Percetiles.
  2. What are fractiles or Quantiles?
  3. How quantiles are computed for grouped and ungrouped data.

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