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Exam 8: Continuous Probability Distributions

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Question 1

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To find the probability for a uniform random variable you take the ____________________ times the ____________________ of its corresponding rectangle.

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base; height
height;...

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Question 2

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The total area under f(x) for a continuous random variable must equal ____________________.

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Let X be an exponential random variable with $\lambda$ = 1.50.Find the following: a. f(x) b. The y-intercept of f(x)

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. -{Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

If the mean of an exponential distribution is 2, then the value of the parameter $\lambda$ is

A random variable with density function e^-xfor x $\ge$ 0 has an exponential distribution whose mean is ____________________.

A continuous random variable X has a uniform distribution between 5 and 25 (inclusive), then P(X = 15) = 0.05.

If X is a continuous random variable on the interval [0, 10], then P(X > 5) = P(X $\ge$ 5).

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -{Electronics Test Narrative} Find the probability that a student will take more than 60 minutes to finish the test.

Suppose X has a chi-squared distribution with 10 degrees of freedom.The variance of X is:

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

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -{Electronics Test Narrative} Find the probability that a student will take exactly one hour to finish the test.

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

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

Suppose you have an F distribution with degrees of freedom 10, 20. a. Find the mean b. Find the variance. c. Find the standard deviation.

The mean of a Student t distribution is ____________________.

A continuous random variable X has a uniform distribution between 5 and 15 (inclusive), then the probability that X falls between 10 and 20 is 1.0.

Light Bulb Lifetime The lifetime of a light bulb (in hours) is exponentially distributed with $\lambda$ = 0.008. -{Light Bulb Lifetime Narrative} What is the mean and standard deviation of the light bulb's lifetime?

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. -{Battery Life Narrative} What proportion of these batteries will last for more than 4,000 hours?

Tanner took a statistics test whose mean was 80 and standard deviation was 5.The total points possible was 100.Tanner's score was 2 standard deviations below the mean.What was Tanner's score, rounded to the nearest whole number?