Chapter 5 Flashcards
Density function
ANy f(x) function that can be used for the probability distribution of a continuous random variable
Density function conditions
- For all numbers f(x)greater or equal to 0, the graph never drops below the x axis
- The area under the region f(x) is 1
Normal distribution
The probability distribution corresponding with a density function for a bell curve with mean and standard deviation parameters
Normal random variable
A continuous random variable that is described by the parameter of normal distribution
Relationship with SD and probability
Inverse relationship (SD increases probability decreases etc.)
Standard normal distribution
A normally distributed random variable with mean of 0 ad SD of 1
Left area
P(Z<z-score)
Right area
- 1-Left area
- P(Z<-z)
Area between
P(z_1<Z<z_2)
P(Z<z_2)-P(Z<z_1)
Finding a standard normal variable for a given area
Probability for general normal random variables
P(a<x<b)=P(zscore of a<Z<zscore of b)
-Z denoted a standard normal random variable
-a can be any number from -inf and above
-b can be any number from inf and below
Tail distribution
A certain max or minimum (x*) is stated by the question and you need to find the probability of that happening
To do this you need to find z* which is just the z-score of x* and then answering the question by finding what value you are trying to find (x* or the value that is min/max for x* to be true)