The Uniform Probability Distribution
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Uniform Distribution Examples The Uniform Probability Distribution Bernd Schröder Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Definition. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Definition. A continuous random variable is said to have uniform distribution on the interval [A, B] if and only if its probability density function is Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Definition. A continuous random variable is said to have uniform distribution on the interval [A, B] if and only if its probability density 1 function is ; for A ≤ x ≤ B, f (x; A, B) = B−A 0; otherwise. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Definition. A continuous random variable is said to have uniform distribution on the interval [A, B] if and only if its probability density 1 function is ; for A ≤ x ≤ B, f (x; A, B) = B−A 0; otherwise. A Bernd Schröder The Uniform Probability Distribution B Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Definition. A continuous random variable is said to have uniform distribution on the interval [A, B] if and only if its probability density 1 function is ; for A ≤ x ≤ B, f (x; A, B) = B−A 0; otherwise. 6 1 B−A ? A Bernd Schröder The Uniform Probability Distribution B Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Definition. A continuous random variable is said to have uniform distribution on the interval [A, B] if and only if its probability density 1 function is ; for A ≤ x ≤ B, f (x; A, B) = B−A 0; otherwise. 6 1 B−A ? A B Example. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Definition. A continuous random variable is said to have uniform distribution on the interval [A, B] if and only if its probability density 1 function is ; for A ≤ x ≤ B, f (x; A, B) = B−A 0; otherwise. 6 1 B−A ? A B Example. RAND() is uniformly distributed on [0, 1]. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≤ 3) Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≤ 3) 2 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≤ 3) 2 3 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≤ 3) 2 3 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≤ 3) 2 3 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≤ 3) 2 3 5 P(X ≤ 3) Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≤ 3) 2 3 5 P(X ≤ 3) = P(2 ≤ X ≤ 3) Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≤ 3) 2 5 3 P(X ≤ 3) = P(2 ≤ X ≤ 3) = Bernd Schröder The Uniform Probability Distribution 1 3 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≥ 4) Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≥ 4) 2 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≥ 4) 2 Bernd Schröder The Uniform Probability Distribution 4 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≥ 4) 2 Bernd Schröder The Uniform Probability Distribution 4 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≥ 4) 2 Bernd Schröder The Uniform Probability Distribution 4 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≥ 4) @ @@ @@ @ @@@@ @ @@@@ @ @ @@@ @ @ @@ @@@ 2 Bernd Schröder The Uniform Probability Distribution 4 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≥ 4) @ @@ @@ @ @@@@ @ @@@@ @ @ @@@ @ @ @@ @@@ 2 4 5 P(X ≥ 4) Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≥ 4) @ @@ @@ @ @@@@ @ @@@@ @ @ @@@ @ @ @@ @@@ 2 4 5 P(X ≥ 4) = P(5 ≥ X ≥ 4) Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(X ≥ 4) @ @@ @@ @ @@@@ @ @@@@ @ @ @@@ @ @ @@ @@@ 2 Bernd Schröder The Uniform Probability Distribution 5 4 P(X ≥ 4) = P(5 ≥ X ≥ 4) = - 1 3 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(3.5 ≤ X ≤ 7) Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(3.5 ≤ X ≤ 7) 2 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(3.5 ≤ X ≤ 7) 2 Bernd Schröder The Uniform Probability Distribution 3.5 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(3.5 ≤ X ≤ 7) 2 Bernd Schröder The Uniform Probability Distribution 3.5 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(3.5 ≤ X ≤ 7) 2 Bernd Schröder The Uniform Probability Distribution 3.5 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(3.5 ≤ X ≤ 7) @@@ @@ @@ @@ @ @@@ @@@ @ @@ @@@@ @ @ @@ @@@@ @@ @ @ @ @@@@@ 2 Bernd Schröder The Uniform Probability Distribution 3.5 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(3.5 ≤ X ≤ 7) @@@ @@ @@ @@ @ @@@ @@@ @ @@ @@@@ @ @ @@ @@@@ @@ @ @ @ @@@@@ 2 3.5 5 P(3.5 ≤ X ≤ 7) Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(3.5 ≤ X ≤ 7) @@@ @@ @@ @@ @ @@@ @@@ @ @@ @@@@ @ @ @@ @@@@ @@ @ @ @ @@@@@ 2 3.5 5 P(3.5 ≤ X ≤ 7) = P(3.5 ≤ X ≤ 5) Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute each of the following probabilities. P(3.5 ≤ X ≤ 7) @@@ @@ @@ @@ @ @@@ @@@ @ @@ @@@@ @ @ @@ @@@@ @@ @ @ @ @@@@@ 2 3.5 5 P(3.5 ≤ X ≤ 7) = P(3.5 ≤ X ≤ 5) = Bernd Schröder The Uniform Probability Distribution 1 2 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. 2 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. 2 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. 2 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. @@@@@ @@ @@ @ @@@@ @@@ @@ @ @ @ @ @@ @ @ @ @@@@ @ @@@ @ @ @ @ @ @ @@ @ @ @ @@ @@@@@@@ 2 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. @@@@@ @@ @@ @ @@@@ @@@ @@ @ @ @ @ @@ @ @ 0.7 @ @ @@@ @ @@@ @ @ @ @ @ @ @@ @ @ @ @@ @@@@@@@ 2 Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. @@@@@ @@ @@ @ @@@@ @@@ @@ @ @ @ @ @@ @ @ 0.7 @ @ @@@ @ @@@ @ @ @ @ @ @ @@ @ @ @ @@ @@@@@@@ 2 x Bernd Schröder The Uniform Probability Distribution 5 Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. @@@@@ @@ @@ @ @@@@ @@@ @@ @ @ @ @ @@ @ @ 0.7 @ @ @@@ @ @@@ @ @ @ @ @ @ @@ @ @ @ @@ @@@@@@@ 2 x 5 0.7 1/3 Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. @@@@@ @@ @@ @ @@@@ @@@ @@ @ @ @ @ @@ @ @ 0.7 @ @ @@@ @ @@@ @ @ @ @ @ @ @@ @ @ @ @@ @@@@@@@ 2 x 5 0.7 = 0.7 · 3 1/3 Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. @@@@@ @@ @@ @ @@@@ @@@ @@ @ @ @ @ @@ @ @ 0.7 @ @ @@@ @ @@@ @ @ @ @ @ @ @@ @ @ @ @@ @@@@@@@ 2 x 5 0.7 = 0.7 · 3 = 2.1 1/3 Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. @@@@@ @@ @@ @ @@@@ @@@ @@ @ @ @ @ @@ @ @ 0.7 @ @ @@@ @ @@@ @ @ @ @ @ @ @@ @ @ @ @@ @@@@@@@ 2 x 5 0.7 = 0.7 · 3 = 2.1 1/3 So x = 5 − 2.1 Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science Uniform Distribution Examples Example. The random variable X is uniformly distributed on [2, 5]. Compute the value x so that P(X ≥ x) = 0.7. @@@@@ @@ @@ @ @@@@ @@@ @@ @ @ @ @ @@ @ @ 0.7 @ @ @@@ @ @@@ @ @ @ @ @ @ @@ @ @ @ @@ @@@@@@@ 2 x 5 0.7 = 0.7 · 3 = 2.1 1/3 So x = 5 − 2.1 = 2.9. Bernd Schröder The Uniform Probability Distribution Louisiana Tech University, College of Engineering and Science
