In Mathematics, a variable can be classified into two types, namely: discrete or continuous. If a variable can take on two or more distinct real values so that it can also take all real values between them (even values that are randomly close together). In this case, the variable is continuous in the given interval. If a variable will take a non-infinitesimal break on each side of it, and it does not contain any values, then it is discrete around that value. In some instances, a variable will hold discrete values in some areas of the number line and continuous in others areas.. Show
Continuous Variable DefinitionA continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite. In continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory. There are two types of continuous variables namely interval and ratio variables.
Instant variableA variable can be defined as the distance or level between each category that is equal and static. For example, what is the average day time temperature in Bangalore during the summer? Ratio variableRatio variable is another type of continuous variable. This type of variable has only one variation from an interval variable. The only difference is that the ratio between the scores gives information regarding the relationship between the responses. Difference between Discrete and Continuous VariableBelow are the main differences between discrete and continuous variables.
Continuous Variable ExampleContinuous variables would take forever to count. In fact, we would get to forever and never finish counting them. For example, take an age. We can’t count “age”. Because it would literally take forever. For example, it could be 37 years, 9 months, 6 days, 5 hours, 4 seconds, 5 milliseconds, 6 nanoseconds, 77 picoseconds…and so on. Discrete and Continuous Random Variables: A variable is a quantity whose value changes. A discrete variable is a variable whose value is obtained by counting. Examples: number of students present number of red marbles in a jar number of heads when flipping three coins students� grade level A continuous variable is a variable whose value is obtained by measuring. Examples: height of students in class weight of students in class time it takes to get to school distance traveled between classes A random variable is a variable whose value is a numerical outcome of a random phenomenon. ▪ 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 ▪ A random variable can be discrete or continuous A discrete random variable X has a countable number of possible values. Example: Let X represent the sum of two dice. Then the probability distribution of X is as follows:
To graph the probability distribution of a discrete random variable, construct a probability histogram. A continuous random variable X takes all values in a given interval of numbers. ▪ The probability distribution of a continuous random variable is shown by a density curve. ▪ The probability that X is between an interval of numbers is the area under the density curve between the interval endpoints ▪ The probability that a continuous random variable X is exactly equal to a number is zero Means and Variances of Random Variables: The mean of a discrete random variable, X, is its weighted average. Each value of X is weighted by its probability. To find the mean of X, multiply each value of X by its probability, then add all the products.
The mean of a random variable X is called the expected value of X. Law of Large Numbers: As the number of observations increases, the mean of the observed values,
The more variation in the outcomes, the more trials are needed to ensure that
Rules for Means: If X is a random variable and a and b are fixed numbers, then
If X and Y are random variables, then Example: Suppose the equation Y = 20 + 100X converts a PSAT math score, X, into an SAT math score, Y. Suppose the average PSAT math score is 48. What is the average SAT math score? Example: Let Let
The Variance of a Discrete Random Variable: If X is a discrete random variable with mean The standard deviation
Rules for Variances: If X is a random variable and a and b are fixed numbers, then
If X and Y are independent random variables, then
Example: Suppose the equation Y = 20 + 100X converts a PSAT math score, X, into an SAT math score, Y. Suppose the standard deviation for the PSAT math score is 1.5 points. What is the standard deviation for the SAT math score? Suppose the standard deviation for the SAT math score is 150 points, and the standard deviation for the SAT verbal score is 165 points. What is the standard deviation for the combined SAT score? *** Because the SAT math score and SAT verbal score are not independent, the rule for adding variances does not apply! What is an infinite number of values in an interval between two specific values?A variable is said to be continuous if it can assume an infinite number of real values within a given interval.
What random variable can assume an infinite number of values in one or more intervals?A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.
Is a random variable that can assume an infinite number of values in an interval between two 2 specific values?Random variables that can assume a countable number (finite or infinite) of values are called discrete. Random variables that can assume values corresponding to any of the points con- tained in one or more intervals (i.e., values that are infinite and uncountable) are called continuous.
What is random variable where the data can take infinitely many values?A continuous random variable is a random variable where the data can take infinitely many values. For example, a random variable measuring the time taken for something to be done is continuous since there are an infinite number of possible times that can be taken.
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What type of variable that assumes an infinite number of values in an interval between two specific values Brainly?
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