Probability Distribution Statistics Random Variables Probability Distribution Questions What is the difference between a discrete random variable and a continuous random variable? What is the sum of the probabilities in a probability distribution? What is an example of a continuous random variable? How are random variables generally identified (i.e., what notation is used to identify a random variable)? What does the term "expected value" mean? What notation is used to designate the expected value of a random variable? You roll three dice, and you define the random variable #X# as the number of heads obtained. What are all possible values of the random variable #X#? You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm for many years, and have created a probability distribution for 0, 1, 2, 3, or 4 people in line. The probabilities are 0.1, 0.3, 0.4, 0.1, and 0.1, respectively. What is the probability that at least 3 people are in line at 3 pm on Friday afternoon? You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm for many years, and have created a probability distribution for 0, 1, 2, 3, or 4 people in line. The probabilities are 0.1, 0.3, 0.4, 0.1, and 0.1, respectively. What is the probability that at most 3 people are in line at 3 pm on Friday afternoon? You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm for many years, and have created a probability distribution for 0, 1, 2, 3, or 4 people in line. The probabilities are 0.1, 0.3, 0.4, 0.1, and 0.1, respectively. What is the expected number of people (mean) waiting in line at 3 pm on Friday afternoon? How is the law of large numbers related to probability? What is an example of the law of large numbers? How do I summarize the possible outcomes of a random variable and their associated probabilities? Is the fuel efficiency (in miles per gallon) of an automobile a discrete or continuous variable? Is the distance that a person throws a baseball a discrete or continuous variable? Is age continuous or discrete data? Is a gallon of orange juice a discrete or continuous variable? Is the blood pressure of a group of student the day before their final exam a discrete or continuous variable? Would the nutrition levels and dietary habits (e.g. high fat diets, high cholesterol levels, protein or low carb diets, vegetarian, vegan, normal eater, etc.) of people in a survey be considered either Discrete or Continuous data? Is the temperature of a cup of coffee sitting on the counter related to the number of minutes since it was poured into the coffee cup a discrete or continuous graph? Suppose that U has a uniform distribution on [0, 1] and that, conditional on U = u, the distribution of V is uniform on [0, u]. What is the probability density function of V? How do you derive a cumulative density function from a probability density function? Can a random variable with a non-continuous cumulative density function have a probability density function? If random variable X has a probability density function of f(x)=1/x on the interval[e,e^2], what is the standard deviation of X? Suppose X has probability density function f(x)=6x(1-x) for 0<x<1 and 0 otherwise. What is E[X] and Var[X]? When is it appropriate to assume that data fits into a Poisson distribution? What is the moment generating function of a Poisson distribution? In terms of the parameters of the probability mass function, what is the formula for the standard deviation of a Poisson distribution? What can a Poisson regression be used to estimate? What is a random walk? Why can stock prices be modeled with a random walk? How do you estimate the mean of a random walk? What is a Markov Chain? If a random variable follows a random walk, is the expected change in its value correlated with its prior changes? The number of cases of tetanus reported in the US in a single month has a Poisson distribution with a parameter of λ= 4.0. What is the probability that exactly one case of tetanus will be reported? What is the difference between Poisson Distribution and Exponential Distribution? Last year a man wrote 142 checks. Let random variable #x# represent the number of checks he wrote in a day, and assume it has a Poisson distribution. What is the mean number of checks written per day? Consider a Poisson distribution with #μ=3#. What is #P(x≥2)#? How do you know when to use a Poisson distribution or binomial distribution? Suppose #X# has a Poisson distribution with a mean of .4. How would i find the probability when #X=0, X=4, X<= 2,# and when #X=8#? Why is a Poisson distribution important? If I roll 2 dice, there are 36 possible outcomes. If #x# is the sum of those two numbers, what would the probability distribution look like? A home has installed 4 security systems to detect attempted break-ins. What is the probability that at least one of the 4 security systems will detect it? How can you find standard deviation from a probability distribution? An exam has two parts. Raul has probability .9 of answering a question from part A correctly and .7 of answering a question from part B correctly. What is the probability that Raul's grade is greater than 75%? What is the difference between probability distribution and sampling distribution? What is the probability distribution of rolling a single die? How do I find the probability density function of a random variable X? The number of surface flaws in a plastic roll used in the interior of automobiles has a Poisson distribution with a mean of 0.06 flaw per square foot of plastic roll. What is the probability that there are no surface flaws in an auto’s interior? Suppose that you get into a car accident at an average rate of about one accident every 3 years. In the next 21 years, you would expect to have about 7 accidents. if you actually had 5 accidents in that time, can you say that you're a better driver? The mean number of oil tankers at a port city is 8 per day. The port has facilities to handle up to 12 oil tankers in day. What is the probability that too many tankers will arrive on a given day? Dutchess County, New York, has been experiencing e mean of 35.4 motor vehicle deaths each year. What is the mean number of deaths per day? What's the difference between a binomial, hypergeometric, and Poisson probability distribution? How do you compute the variance of a probability distribution? What is the formula for the variance of a probability distribution? The number of cases of tetanus reported in the US in a single month has a Poisson distribution with a parameter of λ= 4.0. What is the probability that five or more cases will be reported? How can you recognize a poisson distribution? Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. If one male is randomly selected, what is the probability that his head breadth is less than 6.2 inches? If we were to toss a single die (singular for dice) 1000 times, how many 6s could we expect over the long run? What is the standard deviation? The average age of a college professor is normally distributed with a mean of 40 years and a standard deviation of 8 years. What is the probability that a teacher is older than 50? How do you compute the variance of the probability distribution in the table provided? A fair die is rolled 3 times. A 4 is considered "success", while all other outcomes are "failures". What is the probability of 2 successes? Products from a certain machine are too large 15% of the time. What is the probability that in a run of 20 parts, 5 are too large? Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ = 7. What is the probability P (X > 42)? How do you determine the probability distribution of #P(x=4)#? How do you determine the probability distribution of #P(x>5)#? What is a discrete probability distribution? What two conditions determine a probability distribution? Is the following distribution a discrete probability distribution? If not, why? How do you determine the required value of the missing probability to make the following distribution a discrete probability distribution? What is the probability that the deal of a five-card hand provides a pair of aces? What is the probability that the deal of a five-card hand provides exactly one ace? What is the probability that the deal of a five-card hand provides no aces? What is the probability that the deal of a five-card hand provides at least one ace? What is the difference between discrete probability distribution and continuous probability distribution? Consider the following discrete probability distribution. What is the probability that #x# equals 7? Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.42 year. What is the probability that more than five loads occur during a 3 year period? The number of accidents is .4 accidents / day. What is the probability that the time from now to the next accident will be more than 3 days?What is the probability that the the time from now to the 3rd accident will be more than 5 days? A fair coin is tossed 60 times. Using the normal approximation to the binomial distribution, what is the probability that a head will show between 30 and 36 times inclusive? Question #af719 Question #8b490 If the probability density function of #X# is #f(x) = (1+ax) /2, -1 le x le 1, -1 le a le 1# then the expectation of #X# is? (a) #6/a# (b) #a /3# (c) #a /2# (d) #3/a# Random Variables View all chapters Probability Distribution Mean and Standard Deviation of a Probability Distribution Law of Large Numbers Addition Rules for Variances Next