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

Sandsynlighedsteori og Statistik
Uge 39
Thomas H. Jørgensen
Baseret p˚ a original af Anders Rahbek, Heino Bohn Nielsen og Mette Ejrnæs
Økonomisk 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 nedenunder
1

C.1
A 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 shot
is 0.6?
3. What are the expected value and variance of the number of hits out of 10 shots
if p = 0.5?
C.2
Let X be a random variable with discrete pdf f ( x ) = x/ 8 if x = { 1 , 2 , 5 } , and zero
otherwise. Find:
1. E ( X )
2. V ar ( X )
3. E (2 X + 3)
C.3
At a computer store, the annual demand for a particular software package is a
discrete random variable X . 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 package
is obsolete and the owner loses the investment on the unsold copies. The pdf of X
is given by the following table:
x 0 1 2 3 4
f(x) .1 .3 .3 .2 .1
1. Find E ( X ).
2. Find V ar ( X ).
3. Express the owner’s net profit Y as a linear function of X , and find E ( Y ) and
V ar ( Y ).
2

C.4
The number of calls that arrive at a switchboard during one hour is Poisson distri-
buted with mean μ