The most common coordinating conjunctions are for, and, nor, but, or, yet, and so; you can remember them by using the mnemonic device FANBOYS. I’d like pizza or a salad for lunch. We needed a place to concentrate, so we packed up our things and went to the library.

An independent clause is a sentence. Jim studied in the Sweet Shop for his chemistry quiz. A dependent clause is a group of words that contains a subject and verb but does not express a complete thought.

Independent Clause Examples I enjoy sitting by the fireplace and reading. Waiting to have my car’s oil changed is boring. She wants to travel the world and see wonderful sights. Our planets revolve around the sun.

Hyphens’ main purpose is to glue words together. They notify the reader that two or more elements in a sentence are linked. Although there are rules and customs governing hyphens, there are also situations when writers must decide whether to add them for clarity.

A dependent clause (or subordinate clause) is a clause that cannot stand alone as a complete sentence because it does not express a complete thought.

An independent clause is a sentence that has a subject and a verb and requires no extra information to understand. Dependent clauses, which start with subordinating conjunctions such as “while,” “that,” or “unless,” give background information but cannot stand on their own as sentences.

The quantity that depends on the other quantity is called the dependent variable, and the quantity it depends on is called the independent variable. The values of variables are used in tables and in plotting graphs. In this lesson, we identify the dependent variable and the independent variable in a table or a graph.

The dependent variable is the variable that is being measured or tested in an experiment. For example, in a study looking at how tutoring impacts test scores, the dependent variable would be the participants’ test scores, since that is what is being measured.

You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause, while a dependent variable is the effect. In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable.

You can tell if two random variables are independent by looking at their individual probabilities. If those probabilities don’t change when the events meet, then those variables are independent. As a simple example, let’s say you have two random variables X and Y. X can equal 0, 1, or 2 and Y can equal 0 or 1.

Answer: An independent variable is exactly what it sounds like. It is a variable that stands alone and isn’t changed by the other variables you are trying to measure. For example, someone’s age might be an independent variable.

The first component is the definition: Two variables are independent when the distribution of one does not depend on the the other. If the probabilities of one variable remains fixed, regardless of whether we condition on another variable, then the two variables are independent.

Independent Events: Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur. If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

Independence two jointly continuous random variables X and Y are said to be independent if fX,Y (x,y) = fX(x)fY (y) for all x,y. It is easy to show that X and Y are independent iff any event for X and any event for Y are independent, i.e. for any measurable sets A and B P( X ∈ A ∩ Y ∈ B ) = P(X ∈ A)P(Y ∈ B).

Yes, they are independent.

Two discrete random variables are independent if their joint pmf satisfies p(x,y) = pX (x)pY (y),x ∈ RX ,y ∈ RY . f (x,y) = fX (x)fY (y),−∞ < x < ∞,−∞ < y < ∞.

Property 2 says that if two variables are independent, then their covariance is zero. This does not always work both ways, that is it does not mean that if the covariance is zero then the variables must be independent.

Zero covariance – if the two random variables are independent, the covariance will be zero. However, a covariance of zero does not necessarily mean that the variables are independent. A nonlinear relationship can exist that still would result in a covariance value of zero.

Covariance is a statistical tool that is used to determine the relationship between the movement of two asset prices. When two stocks tend to move together, they are seen as having a positive covariance; when they move inversely, the covariance is negative.

If X and Y are independent variables, then their covariance is 0: Cov(X, Y ) = E(XY ) − µXµY = E(X)E(Y ) − µXµY = 0 The converse, however, is not always true. Cov(X, Y ) can be 0 for variables that are not inde- pendent.

Understanding Variance A large variance indicates that numbers in the set are far from the mean and far from each other. A variance value of zero, though, indicates that all values within a set of numbers are identical. Every variance that isn’t zero is a positive number.

standard normal distribution

Continuous Distributions 1. The distribution of a continuous random variable cannot be specified through a probability mass function because if X is continuous, then P(X = x) = 0 for all x; i.e., the probability of any particular value is zero.

Random variables are classified into discrete and continuous variables. The main difference between the two categories is the type of possible values that each variable can take. In addition, the type of (random) variable implies the particular method of finding a probability distribution function.

In probability and statistics, random variables are used to quantify outcomes of a random occurrence, and therefore, can take on many values. Random variables are required to be measurable and are typically real numbers.

In general, quantities such as pressure, height, mass, weight, density, volume, temperature, and distance are examples of continuous random variables.

Answer: The weight of a fire fighter would be an example of a continuous variable; since a fire fighter’s weight could take on any value between 150 and 250 pounds. Suppose we flip a coin and count the number of heads. The number of heads could be any integer value between 0 and plus infinity.

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 a variable whose value is a numerical outcome of a random phenomenon. A discrete random variable X has a countable number of possible values.

Continuous random variables have numeric values that can be any number in an interval. For example, the (exact) weight of a person is a continuous random variable. Foot length is also a continuous random variable. Continuous random variables are often measurements, such as weight or length.

Discrete data can be further sub-divided into three categories: binary, nominal and ordinal. Binary Data: A binary data only takes on two possible values. For example, lamp is on or lamp is off, answer is true or false, 0 or 1, yes or no etc.