Continuous Random Variables Flashcards
What are two characteristics of continuous random variables?
- May assume any numerical value in one or more intervals
2. Use a continuous probability distribution to assign probabilities to intervals of values
If the probability of x will be in a specific interval of numbers is the area under the curve of what symbol that corresponds to the interval?
f(x)
What are properties of continuous probability distributions ?
- f(x) > or equal to 0 for al x
- The total area under the f(x) curve is equal to 1
Essential point: the area under a continuous probability distribution is a probability
How do you symbolize the probability that x could take any value between the range of a to b in a continuous distribution?
P(a
The three shapes that can be made in a continuous distribution is what?
- Rectangular. The uniform distribution
- Symmetrical and bell shaped- the normal distribution
- Skewed left or right
The uniform distribution (rectangle) characteristics is:
- The probabilities are the same for all possible outcomes
- Symmetrical and area under the distribution is = 1
- The mean and the median are the same
û= a + b / 2
Height= area/width or 1/b-a
What are the characteristics of the normal probability distribution?
The normal distribution mean is in the middle
All central tendency’s are equal
Area under total curve is 1
Area under half the curve is .5
The area in a normal distribution that is one SD from the mean is what percentage of people
68.4 or 34.2 twice
The area in a normal distribution that is two SD from the mean is what percentage of people
27.1 % or 13.55% each side
The area in a normal distribution that is three SD from the mean is what percentage of people
4.2% or 2.1% each
What is the formula for Z?
Z= x-u/SD
What does the symbol lamda mean and when do you use it?
Lamda means a number of events that can occur per given interval
In exponential distribution
