Ugeseddel 3 (uge 39).pdf - Sandsynlighedsteori og Statistik...

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Sandsynlighedsteori og StatistikUge 39Thomas H. JørgensenBaseret p˚a original af Anders Rahbek, Heino Bohn Nielsen og Mette EjrnæsØkonomisk Institut, Københavns Universitet, efter˚ar 2018.Emne:Kapitel 3: Diskrete fordelinger [Forelæsningerne uge 38].Øvelsesgang 1:Forbered opgaverne: C.1, C.2 og C.3 (nedenfor), samt 3.20, 3.24, 3.27 i Sørensen(2015)Ekstra (optional) opgave 3.2 i Sørensen (2015)Øvelsesgang 2:Forbered opgaverne: C.4 og Opgave 1 om forsikring (se nedenfor).Afleveringsopgave til Uge 40:Opgave H nedenunder1
C.1A basketball player shoots 10 shots and the probability of hitting is 0.5 on each shot.1. What is the probability of hitting eight shots?2. What is the probability of hitting eight shots if the probability on each shotis 0.6?3. What are the expected value and variance of the number of hits out of 10 shotsif p = 0.5?C.2LetXbe a random variable with discrete pdff(x) =x/8 ifx={1,2,5}, and zerootherwise. Find:1.E(X)2.V ar(X)3.E(2X+ 3)C.3At a computer store, the annual demand for a particular software package is adiscrete random variableX. The store owner orders four copies of the package at$10 per copy and charges customers $35 per copy. At the end of the year the packageis obsolete and the owner loses the investment on the unsold copies. The pdf ofXis given by the following table:x01234f(x).1.3.3.2.11. FindE(X).2. FindV ar(X).3. Express the owner’s net profitYas a linear function ofX, and findE(Y) andV ar(Y).2
C.4The number of calls that arrive at a switchboard during one hour is Poisson distri-buted with meanμ

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Term
Spring
Professor
Claus thustrup
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