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    Probability, Random Variables, Joint Density Functions, Cumulative Density Functions and Projection Graphs

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    1. Given the joint density function for the random variables X and Y as

    The marginal distribution for the random variable X is

    Answer:

    2. Given the joint density function for the random variables X and Y as

    The marginal distribution for the random variable Y is

    Answer:

    3. The following represents the cumulative distribution function for a random variable X.

    From the graph, find .

    Answer: 0.4

    4. The life span in hours for an electrical component is a random variable X with cumulative distribution function

    Determine the probability density function for X.

    Answer:

    5. Let X be the random variable for the life in hours for a certain electronic device. The probability density function is

    The expected life for a component is

    Answer: 2000 hours

    6. The life, X in hundred of hours, of a certain battery has the following density function

    What is the average life of the battery?
    Answer: 200 hours

    7. The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution

    What is the expected or average time between successive speeders?

    Answer: 0.125 hours

    8. The probability distribution of X, the number of defects per 100 yards of a fabric is given by
    x 0 1 2 3 4
    f(x) 0.45 0.35 0.14 0.05 0.01

    The variance for X is
    Answer: 0.8476

    9. The following represents the projection graph for a probability distribution f(x) of a random variable X.

    What is the value for the variance of X?

    Answer: 1

    10. The following represents the cumulative distribution function for a random variable X.

    What is the expected value of X?

    Answer: 2.2

    11. The life span in hours for an electrical component is a random variable X with cumulative distribution function

    Determine the expected life span for an electrical component.

    Answer: 100

    12. The life span in hours for an electrical component is a random variable X with cumulative distribution function

    Determine the variance for the life span for an electrical component.

    Answer: 10000

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    Probability, Random Variables, Joint Density Functions, Cumulative Density Functions and Projection Graphs are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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