11_Continuous Probability Distributions Part 2-1

3 what is the probability that the demand is between

Info icon This preview shows pages 22–31. Sign up to view the full content.

View Full Document Right Arrow Icon
3. What is the probability that the demand is between 31 and 42? 25 45 1/20 x f(x) 31 42 What is the shaded area? P(31 < X < 42) = (42 - 31)/(45 - 25) = 11 / 20 = 0.55
Image of page 22

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
23 Uniform distribution example: iPad mini Daily demand for iPad mini at the Apple store on Walnut Street is uniformly distributed between 25 and 45. 3. What is the probability that the demand is between 31 and 42? 4. What are the mean and standard deviation? P(31 < X < 42) = (42 - 31)/(45 - 25) = 11 / 20 = 0.55 25 45 1/20 x f(x)
Image of page 23
24 Uniform distribution example: iPad mini Daily demand for iPad mini at the Apple store on Walnut Street is uniformly distributed between 25 and 45. 3. What is the probability that the demand is between 31 and 42? 4. What are the mean and standard deviation? P(31 < X < 42) = (42 - 31)/(45 - 25) = 11 / 20 = 0.55 Mean = (a+b)/2 = (25+45)/2 = 35 25 45 1/20 x f(x)
Image of page 24

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
25 Uniform distribution example: iPad mini Daily demand for iPad mini at the Apple store on Walnut Street is uniformly distributed between 25 and 45. 3. What is the probability that the demand is between 31 and 42? 4. What are the mean and standard deviation? P(31 < X < 42) = (42 - 31)/(45 - 25) = 11 / 20 = 0.55 Mean = (a+b)/2 = (25+45)/2 = 35 Standard Deviation = 25 45 1/20 x f(x) ( b - a ) 2 12 = (45 - 25) 2 12 = 5.77
Image of page 25
26 Exponential Distribution : Time/interval between successive arrivals/ “events of interest” is usually exponentially distributed Examples: Time to arrival of next customer Time to serve a given customer at bank/call-center/check-out Properties and Assumptions: Non-negative R.V. Can assume any value between 0 to +∞ Asymmetric: P(X > x) decreases as x increases, for any x ≥ 0 Related to Poisson distribution (more later) and many queueing systems Exponential distribution: X~Expon(λ)
Image of page 26

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
27 Exponential distribution formula: X~Expon() Characterized by λ : “arrival rate” (avg. rate of events per unit time) PDF CDF P(X≤x) Right tail prob. P(X>x) x Mean: Variance: Stdev: 0 ) ( = - x for e x f x λ λ 0 1 ) ( ) ( - = = - x for e x X P x F x λ 0 ) ( ) ( 1 = = - - x for e x X P x F x λ λ μ 1 ] [ = = X E 2 2 1 ] [ λ σ = = X Var λ σ 1 =
Image of page 27
28 Exponential distribution formula: Example: X~Expon (= 5 cust. per hour) CDF P(X≤x) x 1. P(X≤1) = 2. P(X≤0.5) = 3. P(0.5<X≤1.5)= 4. P(X>2)= Mean: Variance: Stdev: unit? 1 – e-5 = 0.9933 1 – e-2.5 = 0.9179 (1-e-7.5) – (1-e-2.5) = 0.0815 e-10 = 0 (up to 4 digits) 0.2 hours 0.04 hr2 = 0.2 hr λ μ 1 ] [ = = X E 2 2 1 ] [ λ σ = = X Var λ σ 1 =
Image of page 28

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
29 Lab accidents at Drexel occur at an average rate of 3 accidents per month, and the number of accidents follows a Poisson distribution. 1. Describe the distribution and the mean time between accidents. λ =3 accidents per month E(X) = 1/ λ = 1/3 months per accident Exponential distribution example: Sci-fi insurance II
Image of page 29
30 2. What is the probability that there is no accident in the next 2 months? 3. An NSF inspection has been scheduled for the first half of March. What is the probability that there will be no accident during the inspection period?
Image of page 30

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 31
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern