Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/probability-distributions/13-2-12/problems/b/

jmaths

IB Mathematics: Applications and Interpretation HL · 13.2: Probability Distributions · 13.2.12

The sum of two independent Poisson variables Problem set B Answers

Skills

    1. (a) Z ~ Po(7.4)
    2. (b) 0.139
    3. (c) 0.324
    1. (a) The rate is not constant: it is higher at meal times. Both kinds of call rise on a cold or wet evening, so they are not independent.
    2. (b) Illness spreads from pupil to pupil, so the counts are not independent, and the rate changes during the school year, so it is not constant.

In context

  1. 0.439

  2. 0.432

    1. (a) Z ~ Po(26)
    2. (b) 0.252
    3. (c) The rate is not constant: more books are issued after school than during lessons. The counts are not independent: the same students borrow both kinds, and a school project raises both.

Stretch

    1. (a) 9.5
    2. (b) 3.08
    3. (c) 0.671
    1. (a) 4.5
    2. (b) 0.194

jmaths.xyz · AI HL · 13.2.12 The sum of two independent Poisson variables