# 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.

#### 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), ...

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