Exam 8: Continuous Probability Distributions

In practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but very large.

(True/False)

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Question 21

The value of an F distribution with v₁ = 5 and v₂ = 10 degrees of freedom such that the area to its left is 0.95 is 3.33.

(True/False)

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Question 22

If the random variable X is exponentially distributed with parameter $\lambda$ = 2, then the probability that X is between 1 and 2 equals the probability that X is between 2 and 3.

(True/False)

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Question 23

NARRBEGIN: ElectronicsTest Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.NARREND -{Electronics Test Narrative} What is the probability density function for this uniform distribution?

(Short Answer)

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Question 24

If X has an exponential distribution, its is equal to its .

(Essay)

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Question 25

NARRBEGIN: Repair Time Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes.NARREND -{Repair Time Narrative} What is the probability density function for the time it takes a technician to fix a telephone problem?

(Short Answer)

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Question 26

If $P \left( X ^ { 2 } > X _ { 025 , v } ^ { 2 } \right) = 14.4$ , then the number of degrees of freedom v is:

(Multiple Choice)

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Question 27

If X has an exponential distribution with parameter $\lambda$ , then f(0) = ____________________.

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Question 28

Since there is an infinite number of values a continuous random variable can assume, the probability of each individual value is virtually 0.

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Question 29

A X² distribution with 5 degrees of freedom has a mean of and a variance of .

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Question 30

The exponential density function f(x):

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Question 31

NARRBEGIN: Battery Life Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours.NARREND -{Battery Life Narrative} What proportion of these batteries will last between 3,800 and 4,100 hours?

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Question 32

Suppose X is a normal random variable with mean 70 and standard deviation 3. Then P(X = 3) = ____________________.

(Short Answer)

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Question 33

The mean and variance of a X² distribution approach ____________________ as the degrees of freedom increase.

(Short Answer)

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Question 34

The probability that a standard normal random variable Z is less than -3.5 is approximately 0.

(True/False)

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Question 35

Like that of the Student t distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

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Question 36

A probability density function shows the probability for each value of X.

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Question 37

NARRBEGIN: Battery Life Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours.NARREND -{Battery Life Narrative} What proportion of these batteries will last less than 3,600 hours?

(Short Answer)

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Question 38

NARRBEGIN: Subway Waiting Time Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.NARREND -{Subway Waiting Time Narrative} What is the median waiting time for this subway?

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Question 39

The shape of the ____________________ distribution is similar to a normal distribution, except it has more area in the tails.

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Question 40

Showing 21 - 40 of 215

In practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but very large.

The value of an F distribution with v₁ = 5 and v₂ = 10 degrees of freedom such that the area to its left is 0.95 is 3.33.

If the random variable X is exponentially distributed with parameter $\lambda$ = 2, then the probability that X is between 1 and 2 equals the probability that X is between 2 and 3.

NARRBEGIN: ElectronicsTest Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.NARREND -{Electronics Test Narrative} What is the probability density function for this uniform distribution?

If X has an exponential distribution, its is equal to its .

NARRBEGIN: Repair Time Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes.NARREND -{Repair Time Narrative} What is the probability density function for the time it takes a technician to fix a telephone problem?

If $P \left( X ^ { 2 } > X _ { 025 , v } ^ { 2 } \right) = 14.4$ , then the number of degrees of freedom v is:

If X has an exponential distribution with parameter $\lambda$ , then f(0) = ____________________.

Since there is an infinite number of values a continuous random variable can assume, the probability of each individual value is virtually 0.

A X² distribution with 5 degrees of freedom has a mean of and a variance of .

The exponential density function f(x):

NARRBEGIN: Battery Life Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours.NARREND -{Battery Life Narrative} What proportion of these batteries will last between 3,800 and 4,100 hours?

Suppose X is a normal random variable with mean 70 and standard deviation 3. Then P(X = 3) = ____________________.

The mean and variance of a X² distribution approach ____________________ as the degrees of freedom increase.

The probability that a standard normal random variable Z is less than -3.5 is approximately 0.

Like that of the Student t distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

A probability density function shows the probability for each value of X.

NARRBEGIN: Battery Life Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours.NARREND -{Battery Life Narrative} What proportion of these batteries will last less than 3,600 hours?

NARRBEGIN: Subway Waiting Time Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.NARREND -{Subway Waiting Time Narrative} What is the median waiting time for this subway?

The shape of the ____________________ distribution is similar to a normal distribution, except it has more area in the tails.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Multiple Regression

Filters

Exam 8: Continuous Probability Distributions

In practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but very large.

The value of an F distribution with v1 = 5 and v2 = 10 degrees of freedom such that the area to its left is 0.95 is 3.33.

If the random variable X is exponentially distributed with parameter λ\lambdaλ = 2, then the probability that X is between 1 and 2 equals the probability that X is between 2 and 3.

NARRBEGIN: ElectronicsTest Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.NARREND -{Electronics Test Narrative} What is the probability density function for this uniform distribution?

If X has an exponential distribution, its ____________________ is equal to its ____________________.

NARRBEGIN: Repair Time Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes.NARREND -{Repair Time Narrative} What is the probability density function for the time it takes a technician to fix a telephone problem?

If P(X2>X025,v2)=14.4P \left( X ^ { 2 } > X _ { 025 , v } ^ { 2 } \right) = 14.4P(X2>X025,v2​)=14.4 , then the number of degrees of freedom v is:

If X has an exponential distribution with parameter λ\lambdaλ , then f(0) = ____________________.

Since there is an infinite number of values a continuous random variable can assume, the probability of each individual value is virtually 0.

A X2 distribution with 5 degrees of freedom has a mean of ____________________ and a variance of ____________________.

The exponential density function f(x):

NARRBEGIN: Battery Life Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours.NARREND -{Battery Life Narrative} What proportion of these batteries will last between 3,800 and 4,100 hours?

Suppose X is a normal random variable with mean 70 and standard deviation 3. Then P(X = 3) = ____________________.

The mean and variance of a X2 distribution approach ____________________ as the degrees of freedom increase.

The probability that a standard normal random variable Z is less than -3.5 is approximately 0.

Like that of the Student t distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

A probability density function shows the probability for each value of X.

NARRBEGIN: Battery Life Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours.NARREND -{Battery Life Narrative} What proportion of these batteries will last less than 3,600 hours?

NARRBEGIN: Subway Waiting Time Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.NARREND -{Subway Waiting Time Narrative} What is the median waiting time for this subway?

The shape of the ____________________ distribution is similar to a normal distribution, except it has more area in the tails.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Multiple Regression

Filters

The value of an F distribution with v₁ = 5 and v₂ = 10 degrees of freedom such that the area to its left is 0.95 is 3.33.

If the random variable X is exponentially distributed with parameter $\lambda$ = 2, then the probability that X is between 1 and 2 equals the probability that X is between 2 and 3.

If X has an exponential distribution, its is equal to its .

If $P \left( X ^ { 2 } > X _ { 025 , v } ^ { 2 } \right) = 14.4$ , then the number of degrees of freedom v is:

If X has an exponential distribution with parameter $\lambda$ , then f(0) = ____________________.

A X² distribution with 5 degrees of freedom has a mean of and a variance of .

The mean and variance of a X² distribution approach ____________________ as the degrees of freedom increase.