ISYE 3770 Final
Let the letter b be any constant. V(b) is always
0
Suppose we have a continuous random variable over -2 < x < 5. What is P(X = 1)?
0
What is the probability that Z = 0?
0
For any probability density function, f(x), the entire area under the curve, f(x) must be equal to
1
What is the area under the pdf, f(z)?
1
Suppose we have a continuous random variable over -2 < x < 5. What is the mean of X?
1.5
If X is a continuous uniform random variable defined over the range 10 to 20, the mean of X is:
15
Which of the following is true about correlation?
Correlation has no units
Another way to represent the variance of a random variable is:
E(X2) - [E(X)]^2.
The exponential random variable models the distance between successive events in a Poisson process.
TRUE
The hypergeometric distribution is associated with sampling without replacement from a finite population of N objects.
TRUE
The mean and standard deviation of an exponentially distributed random variable are equal.
TRUE
The mean of a continuous random variable is its expected value.
TRUE
The mean of a discrete random variable is its expected value.
TRUE
The negative binomial distribution has mean r/p.
TRUE
In equation 4-12, what is np?
The mean of X
In equation 4-13, what is λ?
The mean of X, The variance of X
In equation 4-12, what is np(1minusp)?
The variance of X
Let the letter b be any constant. E(b) is always
b
When X has the pdf, f(x) = λe-λx for x > 0, P(X > x) =
e^-λx.
How many numerical values can a Binomial random variable, X, have?
n+1
For a Poisson process, if the probability that no events occur in a single interval is p, then the probability that an event occurs in an interval four times as long is:
none of the above
If the random variable, X, has a Poisson distribution with a mean of 4 events per minute, the mean number of events per hour is:
none of the above
The entries in the body of Table III are:
probabilities
A conditional probability distribution does not depend on the values of any other random variables.
FALSE
A probability mass function, f(x), is a non-decreasing function of x.
FALSE
Continuous random variables take on discrete values.
FALSE
Discrete random variables take on values across a continuum.
FALSE
Given an exponentially distributed random variable, X, with pdf f(x) = λe-λx for x > 0, f(1) is the probability that X equal 1.
FALSE
If X and Y are jointly distributed continuous random variables, the mean and variance of X cannot be found from the joint distribution.
FALSE
If X and Y are positively correlated, then there is not a linear relationship between them.
FALSE
If a random variable, X, has only integer values, then the mean, E(X), will always be an integer.
FALSE
If the set of points in two-dimensional space that receive positive probability under the joint distribution of X and Y does not form a rectangle, X and Y are independent.
FALSE
If the variances of two discrete random variables are equal, then the means are equal.
FALSE
In the exponential distribution with parameter λ, the mean and variance are both equal to λ.
FALSE
The cumulative distribution function of a continuous random variable is the probability that the random variable X is greater than or equal to x, where x is a specific value of the continuous random variable X.
FALSE
The normal distribution has two parameters; the mean , and the variance
FALSE
The standard deviation of a continuous random variable is its expected value.
FALSE
The standard deviation of a discrete random variable is the square of its variance.
FALSE
The standard normal distribution has both mean and variance equal to unity.
FALSE
The sum of all of the probabilities associated with each specific value of a continuous random variable equals unity.
FALSE
The variance of a binomial random variable with parameters n and p is p(1 - p).
FALSE
The variance of a discrete random variable is defined as
FALSE
To standardize a normal random variable that has mean and variance we use the formula .
FALSE
When the sample size, n, is large relative to the population size, N, the binomial distribution can adequately approximate the hypergeometric distribution.
FALSE
If X is a hypergeometric random variable with parameters n, K, and N, and p = K/N, then the number of successes and the total number of objects are:
K and N.
Which of the following definitions of X demonstrates that X has the Geometric Distribution?
NONBINARY answers
If X and Y are independent discrete random variables, then
P(X = x|Y = y) = P(X = x)
Determine 1 minus ϕ(z):
P(Z > z)
A Bernoulli trial is a random experiment with only two outcomes, success and failure.
TRUE
A cumulative distribution function can be used to find the probability density function of a discrete random variable.
TRUE
A cumulative distribution function can be used to find the probability mass function of a discrete random variable.
TRUE
A discrete uniform random variable has equal probability assigned to each of its possible values.
TRUE
A marginal probability distribution is the individual probability distribution of one of the random variables in a joint distribution.
TRUE
If X is the number of independent Bernoulli trials until the first success, the distribution of X is geometric.
TRUE
If Y and X are independent random variables, then the correlation between them is zero.
TRUE
If the correlation between the two Y and X is zero, then the random variables are independent.
TRUE
In a Poisson Process, the probability of an event in an interval depends on the length of the interval, but not the location of the interval.
TRUE
The Poisson distribution is widely used as a model of the number of events in an interval.
TRUE
The binomial distribution arises from a series of Bernoulli trials.
TRUE
The covariance of two random variables is a measure of the relationship between them.
TRUE
The cumulative distribution function, F(x), of a discrete random variable is the sum of all of the probabilities that are less than or equal to x, where x is a specific value of the discrete random variable, X.
TRUE
The distribution of the number of Bernoulli trials until the rth success is the negative binomial distribution.
TRUE
The exponential distribution has a lack of memory property.
TRUE
The normal distribution can be used to approximate the binomial distribution if np and n(1-p) are greater than five.
TRUE
The probability density function of a continuous random variable is a simple description of the probabilities associated with the random variable.
TRUE
The probability distribution that describes the simultaneous behavior of two or more random variables is called a joint distribution.
TRUE
The probability mass function of a discrete random variable is a description of the probabilities associated with each possible value of the random variable.
TRUE
The sum of all of the probabilities in a probability mass function equals unity.
TRUE
The variance of a continuous random variable can be written as either:
TRUE
True or False? If X is a Binomial random variable, then we can also obtain the mean and variance using the following equations from section 3-3
TRUE
True or False? If X is a Geometric random variable, then we can also obtain the mean and variance using the following equations from section 3-3:
TRUE
True or False? P(X = 3) can be written as P(X = 3) = {P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)} - {P(X = 0) + P(X = 1) + P(X = 2)}
TRUE
True or False? X, the face value for the throw of a fair die, has the discrete uniform distribution.
TRUE
True or false? If cov(X, Y) ≠ 0, then X and Y are not independent.
TRUE
When X is a discrete random variable, f(x) = P(X = x). When X is a continuous random variable, f(x) ≠ P(X = x). True or False.
TRUE