2.3 Flashcards
What is a parameter?
The values that define a random variable’s probability distribution.
What is the parameter for exponential probability distribution?
Beta which is 1/lambda and is the shape or scale parameter.
What is the continuous random variable?
When the range of values represented by the random variable can be infinite.
What is the probability density function?
This is the probability distribution of the random variable that creates or defines the density as a function of x curve.
What is the probability of an exact value for an exponential distribution probability?
The P(X=x) = 0 because we are looking at the area under the curve which represents the probability and in order to have an area there needs to be space between 2 points. We use integrals to find the area under the curve and the area at individual points is also 0.
What is an exponential distribution probability?
Variables that are represented by this probability distribution are often those that measure the amount of time or distance between events of interest or before an event of interest.
What is the memorylessness probability?
This is a method of writing a conditional probability that involves exponential distribution in a simplified way.
ie., P(X>a I X>b) = P(X>a-b)
What is normal probability distribution?
This is another type of a continuous random variable where we look at normal distribution when the exact distribution value is unknown.
What are the parameters of the normal distribution?
The mean of the normal distribution and the standard deviation of the normal distribution.
What is similar between exponential and normal random variable calculations?
That both calculations involve left or right tails not exact values.
What is the R function for calculating normal functions?
pnorm (x, mean, SD)
Backwards: qnorm (x, mean, SD)
What is standard normal distribution?
The goal is to make probability calculations easier and use in confidence interval estimation and hypothesis testing.
What is the standardized score or z-score?
This score expresses how many standard deviations x is from mean.
