Everything 2 Flashcards
Name the 4 questions to DETERMINE IF AN EXPERIMENT IS BINOMIAL.
- Are there a fixed number of trials?
- Are there only 2 possible outcomes?
- Are the outcomes independent of each other? In other words, does the outcome of one trial (or one toss, or one question) affect another trial?
- Does the probability of success remain the same for each trial? (Question 1: yes, each person has the same chance of voting for Mr. Bush as the last.)
EXPECTED VALUE OF A DISCRETE RANDOM VARIABLE:
- What is an expected value and what is a discrete random variable?
- What is the requirement for the function to have?
- Formula
- how to calculate for a set of a list [44,7,6,23,11] and for a set of probabilities? You toss a fair coin three times. X is the number of heads which appear. What is the expected value?
. An expected value is - basically thinking - the mean of a probability distribution. The discrete random variable means that there is a fixed number the variable can take (p.e. rolling a dice {1,2,3,4,5,6}).
.- The function must stop at a particular value. If it doesn’t converge, then there is no expected value.
Formula: E(x) = Sum xm(x)
-> Basically, all the formula is telling you to do is find the mean by adding the probabilities.
list: just calculate mean
probabilities: E(X) = 0(1/8) + 1(3/8) + 2(3/8) + 3(1/8) = 3/2.
- > Sum of values times their probabilities
How to calculate the MEAN and the STANDARD DEVIATION for a BINOMIAL DISTRIBUTION?
Mean= np # number of trials * probability of success SD= Squareroot from npq # q= 1-p
Write down the binominal Distribution Formula.
Solve that problem: 80% of people who purchase pet insurance are women. If 9 pet insurance owners are randomly selected, find the probability that exactly 6 are women.
P(X)= n! / (n-X)!X! * px * qn-x (nein, nix da bin ich bi! zum x!ten mal. Die Wahrscheinlichkeit, hochgenommen zu werden, ist quasi nix)
= .176
In other words, there is a 17.6% chance that exactly 6 of the respondents will be female.
