What is discrete probability distribution?

What is discrete probability distribution?

1. What is discrete probability distribution?
   2. What conditions must be satisfied in a discrete probability distribution.
   3. A discrete probability distribution assigns probabilities to individual values. To what are probabilities assigned in continuous probability distributions.

Answer Exercises: 5.23, 5.30, 6.6, 6.26 and 6.54

Exercise 5.23: The customer service department for a wholesale electronics outlet claims that 90 percent of all customer complaints are resolved to the satisfaction of the customer. In order to test this claim, a random sample of 15 customers who have filed complaints is selected.

1. Let x = the number of sampled customers whose complaints were resolved to the customer’s satisfaction. Assuming the claim is true, write the binomial formula for this situation.
2. Use the binomial tables (see Table A.1, page 783) to find each of the following if we assume that the claim is true:[unique_solution]

• P(x ≤ 13).
• P(x > 10).
• P(x ≥ 14)
• P(9 ≤ x ≤ 12).
• P(x ≤ 9).

1. Suppose that of the 15 customers selected, 9 have had their complaints resolved satisfactorily. Using part b, do you believe the claim of 90 percent satisfaction? Explain.

Exercise 5.30: Suppose that x has a Poisson distribution with µ = 2.

1. Write the Poisson formula and describe the possible values of
2. Starting with the smallest possible value of x, calculate p(x) for each value of x until p(x) becomes smaller than .001.
3. Graph the Poisson distribution using your results of
4. Find P(x = 2).
5. Find P(x ≤ 4).
6. Find P(x ˂ 4).
7. Find P(x ≥ 1) and P(x > 2).
8. Find P(1 ≤ x ≤ 4).
9. Find P(2 ˂ x ˂ 5).
10. Find P(2 ≤ x ˂ 6).

Exercise 6.6: Suppose that the random variable x has a uniform distribution with

c = 2 and d = 8.

1. Write the formula for the probability curve of x, and write an interval that gives the possible values of

1. Graph the probability curve of x.

1. Find P(3 ≤ x ≤ 5).

1. Find P(1.5 ≤ x ≤ 6.5).

1. Calculate the mean µ_x, variance σ²_x, and standard deviation σ_x.

1. Calculate the interval [µ_x ± 2σ_x]. What is the probability that x will be in this interval?

Exercise 6.26: Suppose that the random variable x is normally distributed with mean µ = 1,000 and standard deviation σ = 100. Sketch and find each of the following probabilities:

1. P(1,000 ≤ x ≤ 1,200).
2. P(x > 1,257).
3. P(x ˂ 1,035).
4. P(857 ≤ x ≤ 1,183).
5. P(x ≤ 700).
6. P(812 ≤ x ≤ 913).
7. P(x > 891).
8. P(1,050 ≤ x ≤ 1,250).

Exercise 6.54: Suppose that the random variable x has an exponential distribution with λ = 2.

1. Write the formula for the exponential probability curve of What are the possible values of x?

1. Sketch the probability curve.

1. Find P(x ≤ 1).
2. Find P(.25 ≤ x ≤ 1).

1. Find P(x ≥ 2).

1. Calculate the mean, µ_x, the variance, σ²_x, and the standard deviation, σ_x, of the exponential distribution of x.

1. Find the probability that x will be in the interval [µ_x ± 2σ_x].

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