# Probability function, distribution, value of random variable

Answer the following questions and show your work.

1. Test the following function to determine whether it is a probability function:

P(x) = (x²+5)/80 ; for 1,2,3,4, or 5.

2. A small bag of M&M candies has the following assortment: red(10), blue(2), orange(5), brown(12), green(0), and yellow(8). Give the probability distribution of x.

3. In order to monitor the quality of a production process, samples of size five are selected daily. The random variable of interest is the number of defectives in the five items selected. What values are possible for this random variable?

4. Is the number of textbooks you bought this semester a discrete or continuous random variable? Explain.

5. Given that the numbers 1 through 6 are equally likely to occur, what is Px(â?¤2)? Remember that <= means equal to or less than.

6. Which of the following would not be a continuous random variable?

A) Age of student upon graduation from college.

B) Number of attempts to make a field goal in football.

C) Number of miles driven on a trip.

D) Body temperature of small children.

True or Fales.

7. _____The probability of event A or B is equal to the sum of the probability of event A and the probability of event B when A and B are mutually exclusive events.

8. _____The sum of all probabilities in any probability distribution is always exactly 1.25.

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#### Solution Preview

Please see the answers.

1. Test the following function to determine whether it is a probability function:

P(x) = (x²+5)/80 ; for 1,2,3,4, or 5.

For a Probability density function, the P(x) should be non negative and =1.

x P(X=x)

1 0.075

2 0.1125

3 0.175

4 0.2625

5 0.375

Total 1

Here above two conditions are true. Thus (x) = (x²+5)/80 is a probability density function.

2. A small bag of M&M candies has the following assortment: red(10), blue(2), orange(5), brown(12), green(0), ...

#### Solution Summary

Answers to questions related to Probability function, distribution, value of random variable are given in the answer.

Probability, Random Variables, Joint Density Functions, Cumulative Density Functions and Projection Graphs (12 Problems)

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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