Random Variables

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.

MCQs Random Variable Quiz

• 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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 The post is about MCQ Random Variables. There are 20 multiple-choice questions related to random experiments, random variables and types of random variables, expectations, discrete random variables, and continuous random variables. Let us start with the MCQ Random Variables Quiz.

Please go to Important MCQ Random Variables 1 to view the test

MCQ Random Variables Quiz

•  If $X$ is a continuous random variable, then function $f(X)$ is
• A variable (Random Variable) assuming an infinite number of values is called
• A variable whose value is determined by the outcome of a random experiment is called
• If $X$ and $Y$ are random variable then $E(X + Y)$ is equal to
• If $X$ is a discrete random variable, the function $f(X)$ is
• When four coins are tossed, the value of a random variable (Numbers of head) is
• A variable (Random Variable) assuming a finite number of values is called
• If $X$ and $Y$ are independent random variables then $E(XY)$ is equal to
• Two random variables $X$ and $Y$ are said to be independent if:
• If $X$ and $Y$ are two independent variables, then
• A continuous random variable is a random variable that can
• If $X$ is a random variable that can take only non-negative values, then
• For a random variable $X$, $E(X)$ is
• If $C$ is a non-random variable, the $E(C)$ is
• A continuous variable is a variable that can assume
• A ———– random variable has a countable number of possible values.
• Which of the following statements accurately describes a key difference between discrete and continuous random variables?
• Which of the following are examples of discrete random variables?
• Which of the following statements describes continuous random variables?
• If $X$ is a random variable and $a$ and $b$ are constants then $Var(aX+ b)$ is equal to

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Introduction to a Random Variable in Statistics

A random variable in statistics is a variable whose value depends on the outcome of a probability experiment. As in algebra, random variables are represented by letters such as $X$, $Y$, and $Z$. A random variable in statistics is a variable whose value is determined by chance. A random variable is a function that maps outcomes to numbers. Read more about random variables in Statistics: Random Variable.

Random Variable in Statistics: Some Examples

• T = the number of tails when a coin is flipped 3 times.
• s = the sum of the values showing when two dice are rolled.
• h = the height of a woman chosen at random from a group.
• V = the liquid volume of soda in a can marked 12 oz.
• W = The weight of an infant chosen at random in a hospital.

Key Characteristics of a Random Variable

• Randomness: The value of a random variable is determined by chance.
• Numerical: It assigns numbers to outcomes.
• Function: It is technically a function that maps outcomes to numbers.

Types of Random Variables

There are two basic types of random variables.

Discrete Random Variables: A discrete random variable can take on only a countable number of values. It can have a finite or countable number of possible values.

Continuous Random Variables: A continuous random variable Can take on any value within a specified interval. It can take on any value in some interval.

Examples of Discrete and Continuous Random Variables

• The variables $T$ and $s$ from above are discrete random variables
• The variables $h$, $V$, and $W$ from above are continuous random variables.

Importance of Random Variables in Statistics

Random variables are fundamental to statistics. Random variables allow us to:

• Use mathematical tools to analyze uncertain events.
• Model the real-world phenomena.
• Calculate probabilities of events.
• Compute expected values and variances.
• Make statistical inferences.

Random variables form the basis for probability distributions and are fundamental to statistical inference. Random variables provide a bridge between the real world of uncertainty and the mathematical world of probability.

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