discexamp

discexamp - More Examples (Sections 3.1 to 3.3 Reviewed)...

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More Examples (Sections 3.1 to 3.3 Reviewed) Example 1 The number of pumps in use at both a six-pump station and a four-pump station will be deter- mined. Give the possible values for each of the following random variables. a. T = the total number of pumps in use. Solution T : 0 ; 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9 ; 10 b. X = the di¤erence between the numbers in use at stations one and two. Solution X : ¡ 6 ; ¡ 5 ; ¡ 4 ; ¡ 3 ; ¡ 2 ; ¡ 1 ; 0 ; 1 ; 2 ; 3 ; 4 ; 5 ; 6 c. U = the maximum number of pumps in use at either station. Solution U : 0 ; 1 ; 2 ; 3 ; 4 ; 5 ; 6 d. Z = the number of stations having exactly two pumps in use. Solution Z : 0 ; 1 ; 2 Example 2 A contractor is required by a county planning department to submit one, two, three, four, or …ve forms (depending on the nature of the project) in applying for a building permit. Le Y = the number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y – that is, p ( y ) = ky for y = 1 ; 2 ; 3 ; 4 ; 5 . a. What is the value of k ? Solution For p ( y ) to be a valid pmf, 5 X y =1 p ( y ) = 1 . Therefore: 5 X y =1 p ( y ) = 5 X y =1 ky = k 5 X y =1 y = k (1 + 2 + 3 + 4 + 5) = 15 k = 1 : Hence k = 1 15 . b. What is the probability that at most three forms are required? Solution P ( Y · 3) = p (1) + p (2) + p (3) = 1 15 + 2 15 + 3 15 = 6 15 = 0 : 4 : c. What is the probability that between two and four forms (inclusive) are required?

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This note was uploaded on 01/08/2012 for the course EXST 4050 taught by Professor Staff during the Fall '10 term at LSU.

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discexamp - More Examples (Sections 3.1 to 3.3 Reviewed)...

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