Ugeseddel 3.pdf - Anders Rahbek Heino Bohn Nielsen Mette...

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Anders RahbekHeino Bohn NielsenMette Ejrn°s±konomisk Institut, Klbenhavns UniversitetEfter²r 2017Sandsynlighedsteori ogStatistikjUge 39Emne:Kapitel 3: Diskrete fordelinger [Forel°sningerne uge 38].°velser Uge 39:°velsesgang 1 Uge 39:°Forbered opgaverne: ex. C.1, C.2 og C.3 (nedenfor), 3.20, 3.24, 3.27.°Ekstra opgave 3.2 (optional)°velsesgang 2 Uge 39:°Forbered opgaverne: C.4 og opgaven om forsikring (se nedenfor).1
Ex. C.1A basketball player shoots 10 shots and the probability of hitting is 0.5 oneach shot.a) What is the probability of hitting eight shots?b) What is the probability of hitting eight shots if the probability on eachshot is 0.6?c) What are the expected value and variance of the number of hits out of 10shots if p = 0.5?Ex. C.2LetXbe a random variable with discrete pdff(x) =x=8ifx=f1;2;5g,and zero otherwise. Find:a)E(X)b)V ar(X)c)E(2X+ 3)Ex. C.3At a computer store, the annual demand for a particular software packageis a discrete random variableX. The store owner orders four copies of thepackage at $10 per copy and charges customers $35 per copy. At the end ofthe year the package is obsolete and the owner loses the investment on theunsold copies. The pdf ofXis given by the following table:x01234f(x).1.3.3.2.1a) FindE(X).b) FindV ar(X).c) Express the owner³s net pro´tYas a linear function ofX, and ´ndE(Y)andV ar(Y).Ex. C.4The number of calls that arrive at a switchboard during one hour is Poissondistributed with mean°= 10. Find the probability of occurrence during anhour of each of the following events:2
a) Exactly seven calls arrive.

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