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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

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

The marginal distribution for the random variable Y is

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

From the graph, find .

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.

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

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?

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?

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

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?

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

What is the expected value of X?

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.

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.