Chapter 5 assign.
Which of the following are examples of a binomial experiment?
Ask 12 randomly-selected people whether they are members of Facebook. Ask 27 customers at a movie theater if they spent $20 or more on concessions. Reason: There are more than two outcomes for other experiment.
Suppose there is a jar with 3 red and 3 white marbles in it. If you wanted to know what the probability would be for you to select two marbles randomly (without replacement) and get one marble of each color, what probability distribution would you use?
Hypergeometric
Which distribution provides the most accurate probabilities for the number of successes when we sample without replacement from a population whose size N is not significantly larger than the sample size n?
Hypergeometric since the probability of success p changes noticeably from trial to trial
Generally, a person who is risk averse
demands a reward for taking risk.
The variance for probability distribution measures spread around the
mean.
A Poisson random variable describes the number of successes of a certain event
over a given interval of time or in space.
The expected value of a distribution is also referred to as the
population mean.
The probability distribution that describes a discrete random variable is called a
probability mass function.
When calculating the variance and standard deviation for a discrete random variable, the squared differences about the mean are
weighted by the probabilities of each value.
For a discrete random variable, the variance of X is calculated as
∑(xi−μ)2P(X=xi)
For a discrete probability distribution, which best describes the probability of each value x?
0 ≤ P(X = x) ≤ 1
What are the two key properties of a discrete probability distribution?
0 ≤ P(X = x) ≤ 1 and ∑P(X=xi) = 1
Which distribution is appropriate when counting the number of successes in n trials if the probability of success p remains constant from trial to trial?
Binomial Reason: Poisson counts successes but there's no maximum number of successes n. Reason: Hypergeometric is appropriate when the probability p changes.
All of the following are conditions of a binomial experiment (Bernoulli process) EXCEPT:
For each trial, the probability of a 'success' equals the probability of a 'failure'. Reason: This implies that the probability of 'success' is 0.50 and the probability of 'failure' is 0.50. This is not a necessary condition.
What is the common notation for random variables?
It is common to denote random variables by upper-case letters and particular values of the random variables by the corresponding lower-case letters.
A cumulative distribution function explicitly displays
P(X≤x).
Suppose the expected value of a risky transaction is $1,000 and the value of a no-risk transaction is also $1,000. What type of consumers would be willing to engage in the risky transaction?
Risk neutral. Reason: A risk averse consumer needs a greater reward in order to engage in the risky transaction.
The binomial formula consists of three parts. Which one of the following is not part of the formula?
The conditional probability of a success given a failure. Reason: Trials are independent -- so, conditional probabilities aren't needed.
All of the following are features of a discrete uniform distribution EXCEPT:
The distribution is bell-shaped. Reason: Since each value of a discrete uniform distribution is equally likely, the distribution is "flat" instead of bell-shaped.
Which of the following statements is NOT true?
The number of bankruptcies that are filed in a month is an example of a binomial random variable.
Which of the following are examples of discrete random variables?
The number of bedrooms in a randomly selected house. The number of students who earn an "A" on their statistics exam Reason: This number is countable, and so discrete.
In the following scenarios, indicate those that describe a Poisson random variable.
The number of customers who purchase concessions over the next hour at a movie theater. The number of leaks in a specified stretch of a pipeline. Reason: others are binomial.
Which of the following can be represented by a discrete random variable?
The number of defective light bulbs in a sample of five bulbs
All of the following are characteristics of a Poisson process EXCEPT:
The number of successes in n trials is an integer between 0 and n.
Since there are only two outcomes, 'success' and 'failure,' what must be true about their probabilities?
The probabilities must add to one.
A discrete random variable X may assume an
a countable number of distinct values.
The expected value of the discrete random variable X is
a weighted average of all possible values of X.
A contestant on a game show has a choice between taking $1,500 in cash or a prize hidden behind a curtain. The prize behind the curtain could be worth thousands of dollars or nothing. The expected value of the prize behind the curtain is $2,500. If the contestant is risk neutral, then the contestant will
choose the prize because its expected value exceeds the risk-free cash value of $1,500.
Let X = the side showing when a die is rolled. X is assumed to follow a uniform distribution because
each value of X has the same probability.
The variance for any discrete random variable is found by weighting the squared deviations about the mean by the respective probabilities. This can be simplified for the binomial random variable by
multiplying the number of trials by the probability of a success and the probability of a failure.
The expected value for any discrete random variable is found by summing up the product of the values of the random variables and their respective probabilities. This can be simplified for the binomial random variable by
multiplying the probability of a success by the number of trials.
A function that assigns numerical values to the outcomes of a random experiment is called a ______.
random variable
When calculating the probability of x successes in n trials of a binomial experiment, the probability of success and the probability of failure
remain the same, even when a probability is calculated for a different value of x.
