ISYE 3770 Final

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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


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