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STUDY SHEET for MIDTERM #2 (Wednesday, October 18)
The best way to prepare to the midterm is to read the book and to do the homework exercises. Please, take time to go over the material.
Here is what you have to have an idea about:
- Probability experiment, outcome, sample space, events.
- Probability definition (Classical, Empirical, and Subjective).
- Basic probability rules.
- The addition rules for probability.
- Mutually exclusive events.
- The multiplication rules.
- Conditional probability.
- Independent, dependent events.
- Counting: fundamental counting rule, factorial formulas, permutations rule, and combinations rule.
- Random variable. Probability distribution of a discrete random variable. Its properties.
- The mean, variance, and standard deviation of a discrete probability distribution. Expected value.
- The Binomial probability distribution. Table B.
- The mean, variance, and standard deviation for the Binomial distribution.
- Continuous distributions, probability density curve, area property of a probability density curve.
- The Normal distributions (ND) and its properties; the Standard ND (SND), the standard units (z-scores). Finding area under the SND curve. Table E.
- Applications of the ND. Finding data values given specific probabilities.
- Determining normality.
- Distribution of the Sample Mean. Sampling error.
- The Central Limit Theorem and its applications.
- Finite population correction factor.
- The normal approximation to the Binomial distribution. Correction for continuity.
Below is the list of typical problems in the most general from which you can expect on the test:
Given a random experiment, find the corresponding sample space. {4.2} Given an event, find its probability by using classical definition of probability. {4.2}
Given an event, find its probability by using empirical definition of probability. {4.2}
Given an event, find the probability of its complement. {4.2}
Given two events, determine whether they are mutually exclusive. {4.3}
Given two events, find the probability that either one of them occur. {4.3}
Given two events, find the probability that both of them occur. {4.4}
Given two events, find the probability of one of them given the other. {4.4}
Given two events, show whether they are independent or not. {4.4}
Use Fundamental Counting Rule to find in how many ways the sequence of n events is completed. {4.5}
Calculate the number of possible arrangements of n distinct objects (Factorial Rule).
Calculate in how many ways r elements can be taken from the set of n distinct elements (repetitions are not allowed). [Permutations if the order is essential] {4.5}
Calculate in how many ways r elements can be taken from the set of n distinct elements (repetitions are not allowed). [Combinations if the order is not essential] {4.5}
Given a function, check if it can serve is a discrete probability distribution for some random variable. {5.2}
Given a discrete probability distribution, find its mean, variance, and standard deviation. {5.3}
Find the expected value of a discrete random variable. {5.3}
Given Binomial distribution random variable, find the probability of a certain event {5.4}
Find the mean and standard deviation of the Binomial distribution. {5.4}
List the properties of a Normal probability distribution. {6.2}
- If a binomial distribution problem has p = 0.3 and n = 100, then the mean of this probability distribution is: a) 30 b) 50 c) 200 d) can not be determined
Fill in Blank Questions:
- The probability that a train leaves on time is 0.9 and the probability that it both leaves on time and arrives on time is 0.75. If the train leaves on time, the probability that it also arrives on time is __________________________________________________.
- The number of permutations of n distinct objects taken all together is ____________.
- A random variable that can take on only a finite number of values or a countable infinity of values is called _____________________ random variable.
- The mean of the probability distribution f(x) for which f(x) = 12
x + 2 , for x = 1, 2, 3 is
_____________________________.
- The total area under any normal curve is always equal to __________________.
- The sampling distribution of the mean can usually be assumed to be approximately normal if n is at least _______________________.
