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Let x = number of heads when two unbiased coins are tossed. X is a random variable.
The sample space is {HH,HT,TH,TT} where H = heads and T=tails.
Here is the probability distribution of X.
x-------p(x)
0-------1/4
1-------2/4=1/2
2-------1/4
X assumes 3 values 0,1, and 2 with probabilities 1/4,1/2. amd 1/4.
Which of the following is a valid probability distribution for a discrete random variable?
A.1.0B.0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1E.0.21, 0.16, 0.05, 0.04, 0.03, 0.12, 0.21, 0.18
no
C.0.18, 0.12, 0.03, -0.08, 0.21, 0.04, -0.34, 0.05, 0.16, 0.25, 0.21, 0.17D.0.02, 0.03, 0.21, 0.16, 0.04, 0.12, 0.18, 0.05, 0.16, 0.05
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Define a normal random variable?
I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.
How do you define a variable?
I define an variable by saying x- an value
Difference between continuous and discrete variables?
Continuous variable is one like temperature, and discrete variable are ones like male and female. So if you are looking at temperatures between 90 and 100 degrees, there is an infinite number of them. Say between 99 and 99.1, we have 99.05 and between that and 99 we have 99.005 etc. The variable is continuous because it can take on any value between 90 and 100. But if you are talking about gender, than it is either male of female and not continuous. Having said all this, now we define a continuous variable A continuous is one for which, within the limits the variable ranges, any value is possible. So what about time? If the variable is how long it take to read this answer, is that discrete? NO, it is continuous. A five point scale is an example of a discrete variable.
What number is q for?
It can represent anything that you want - provided that you define it as such. Here are some examples:Algebra: it could represent a typical element in the set of rational numbers.Geometry: In the Cartesian plane (or space), it could represent the ordinate (second coordinate) of a point.Probability: It could represent the probability of the complement of a given event - particularly for the binomial distribution.
What does it mean to define a variable?
State what the variable represents in the equation.
Define a normal random variable?
I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.
What is the probability that the random variable has a value less than 5?
That depends on the rules that define the random variable.
Define p-value vs - z score?
The p-value is the probability of any event or the level of significance for any statistical test. The z-score is a transformation applied to a Random Variable with any Normal distribution to the Standard Normal distribution.
Is the mean of probability distribution is called its expected value?
No. The mean is the expected value of the random variable but you can also have expected values of functions of the random variable. If you define X as the random variable representing the result of a single throw of a fair die, the expected value of X is 3.5, the mean of the probability distribution of X. However, you play a game where you pay someone a certain amount of money for each throw of the die and the other person pays you your "winnings" which depend on the outcome of the throw. The variable, "your winnings", will also have an expected value. As will your opponent's winnings.
What are the differences between density and distribution?
Density refers to the concentration of a particular variable within a specific region or area, such as the number of people per square mile. Distribution, on the other hand, describes how values of a variable are spread out across a dataset or population, such as a normal distribution or skewed distribution. Essentially, density focuses on the amount of a variable present in a given area, while distribution looks at how the values of a variable are spread out across a broader context.
How do you define a variable?
I define an variable by saying x- an value
Difference between continuous and discrete variables?
Continuous variable is one like temperature, and discrete variable are ones like male and female. So if you are looking at temperatures between 90 and 100 degrees, there is an infinite number of them. Say between 99 and 99.1, we have 99.05 and between that and 99 we have 99.005 etc. The variable is continuous because it can take on any value between 90 and 100. But if you are talking about gender, than it is either male of female and not continuous. Having said all this, now we define a continuous variable A continuous is one for which, within the limits the variable ranges, any value is possible. So what about time? If the variable is how long it take to read this answer, is that discrete? NO, it is continuous. A five point scale is an example of a discrete variable.
How do mathematicians define a variable?
They define a variable by saying n equals some value.
What number is q for?
It can represent anything that you want - provided that you define it as such. Here are some examples:Algebra: it could represent a typical element in the set of rational numbers.Geometry: In the Cartesian plane (or space), it could represent the ordinate (second coordinate) of a point.Probability: It could represent the probability of the complement of a given event - particularly for the binomial distribution.
What does it mean to define a variable?
State what the variable represents in the equation.
What is done to a variable represent an unknown quantity?
define
What is a z score and what its used for?
The Normal probability distribution is defined by two parameters: its mean and standard deviation (sd) and, between them, these two can define infinitely many different Normal distributions. The Normal distribution is very common but there is no simple way to use it to calculate probabilities. However, the probabilities for the Standard Normal distribution (mean = 0, sd = 1) have been calculated numerically and are tabulated for quick reference. The z-score is a linear transformation of a Normal variable and it allows any Normal distribution to be converted to the Standard Normal. Finding the relevant probabilities is then a simple task.
