How do you distinguish between a discrete random variable and a continuous random variable?
Compare and contrast probability histograms and density curves.
If X is discretely distributed for the integers {1, 2, 3} and P(X=1) does not equal P(X=3), does the expected value of X have to be an integer? Why or why not? Does the mode have to be an integer? Why or why not? Does the expected value of a distribution have to be a value of x from your distribution (for instance, does the average number of pips on one die rolled have to be 1, 2, 3, 4, 5, or 6)? Does the mode have to be an observed value of x? Why or why not?
How does the Law of Large Numbers relate to the Kid-sino lab on November 18th?
The mean of the sum is the sum of the means.
The variance of the sum is the sum of the variances (if the variables are independent).
The variance of the difference is the SUM of the variances (if the variables are independent).
Why?
The variance of 2X is 4 times the variance of X.
The variance of (X + Y) is the variance of X plus the variance of Y (if the variables are independent).
Why are these different formulas? Or are they?
Have a super day.
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Mrs. L
Within part (a) it says "the payoff X on a single play." What are they saying that X represents? What possible outcomes are there for X? What is the probability of each one?
For problem 7.15 the problem states that "statistic [p-hat] is a random variable that is approximately normally distributed with mean [mu] = .15 and standard deviation [sigma] = .0092." You can ignore the confusing symbol because it isn't important right now, just treat it like X. Pretending that the random variable is X, X~N(.15, .0092), and you just calculate z scores, etc.
For problem 7.18, you're only selecting one number. The people running the game select 20. You win if your number is one of those 20 selected. The authors calculated the probability for you, but I hope tht you could calculate this on your own.
Re-reading the problems will help you develop good interpretation skills.
See you Friday--and at CiCi's onSunday????
RE: Continuous random variables
Distributions can be continuous or discrete and finite or infinite.
If you can't possibly begin to list all of the possible values that X can take (for instance, the exact age of a student), then you have a continuous random variable. For any two ages that you might list, there would always be infinitely many values in between those two ages. These distributions can go on forever (infinite) or they can end at a particular value of X (finite).
On the other hand, if you can begin a list that would never end, like the number of coins you would have to flip until you got ten heads in a row, it is discrete and infinite because there's no such thing as the 15 and a half-th flip and because the count might go on forever. If you can't subdivide the values of X, then the distribution is discrete.
The sample space (the list of all of the possible outcomes) was given. Each of those ourcomes was equally likely (1/3 probabiliity). Let X be the total of the two cards. What would the totals of the two cards be?
Put the values together in the form of a discrete probability distribution as we did in class.
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