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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 does it mean to define a variable?
State what the variable represents in the equation.
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.
