# ECON 3818 Study Guide - Fall 2019, Comprehensive Final Exam Notes - Yit, Wimt, Vjing

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Fall 2017
Recitation
2 -
Danny
Kurban
09/11-09/
14
University
of
Probability
distributions,
expected
value
~
cjo
-f1
fl~
'CJD
ft
...
o
.~
r
~
f>O
F
1.
Pati
e
nts
arrive
at
a hospital emergency room
at
a rate
of
6 patients per hour. Let A be t he
average
number of
patients
per
time
interval,
and
let ix
be
the number of patients
that
arrive in some given time in
te
rva
l.
(a) Which of
the
two variables is a random variable, and which is a param
ete
r?
rf"
· \ I A. "-
Cl)V\
',10-,._
t
,-
(,
"'"
"')
(,
.
Joe
~,« c
l-.~~j
-u
(h)
What
probability di
st
ribution does X take?
Wh
at
is
the
probability mass function (pmf) for
thi
s di
st
ribu-
tion?
Po
\
'>S
o
f/\,
o
'.i.1
1
'.
bv
:to
V\.
(-:ti-
o
-t
~i,vo.
\s
-
1"'-
f,
vlu
-
,v-.id
V<k
()
l
~11
vrts
J
p~,
e"-;,.~
p(
t =
~)
--;::
(c)
What
is
the
probability
that
exactly 7 patients arrive in 1 hour?
- b 'I
nci
-a
?J
: e b ,
?\
4
r ?:
v1 I
(d)
Wh
at
is
th
e probability
that
exactly 7 patients arrive in 90 minutes?
-
'7
"-'
{,
,','>
: 9
P
(x,?)r
e q .
r,
: 0,
12
2.
Let
~~
N(0
,
1)
= N (
f>-
,
er-
1
)
l (
"'-
'
\J._l
,(}J,\(__tt...
~
-~
~
? · ·
ia
6 . ? H d
11
h h
(a)
What
is
th
e
nam
e
of
this distribution. 1s
1t
E!ffllcrete
or contmuous.
ow
o
we
ca
t e p
ar
arnters t at
take on the value
:;
0 and 1 in this case?
I ' I
S
toj\!o.,dv
V\
Of
t.11.II
I
£1
,'>
\ f'
1c,
.,.
-,
OIi'-'
Co
_,,-i
.
v'lv-
0\.A~
(h) Find
th
e probability
that
Z >
l.
(c) Find
th
e
prob
ability
that
2 < Z < 6.
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3.
Suppose X ~
N(µ,
q2
),
with µ = 8 and q2 = 4.
(a)
What
is
the
relevant z-statistic
wh
en looking
for
P (X \$ 5)? R
111-'t~1
b"r
z ~ N (O, I).
'l
"'tJl0
.1
):
-x,-/:!:_:
~ .
-t
~ - 4
(.T
:a.
-
(b) Based on
thi
s z-statistic,
wh
at
is
P(X
\$ 5)?
P(t-H)
: p (
'fi-s
~
1-
-¾0
vv,..,.,-
, J 0
p \
~
!
3)
· J o bb
(.\
i'..
(c)
What
is
P(X
= 5)? Explain.
P(
x..=
r;)
= 0
~
~
,fo
,
<J..v.y
to111f
,
v.1>ov-
,
:J.
\
'>
tt
~
bv-t
'
,orv
,
-t
1->v
~
n>
b
a.b
'k
ft'
o/~
j o
"Vle-
eµ.c.~
va.l~
~s
e
:""
l ,
..
~
4. Suppose X
is
distributed such t
hat
f(x) = 3x2
for
O
:5
X \$ 1, O elsewhere.
(a)
Pr
ove this is a proper probabili
ty
distribution.
ah,•ay
s
~v
t- -t.o i
...
-rc.,
,
0-1~
-to
{
(b) Fiud the
CDF
of
X.
(c) Fiud
P(X
:5
1/2).
I )
F(+)
P(")(,S""i
: -
f''(
l
~
p((C~
O)
~
p
(-x._0)
-
p(1,(
t)
~
p(1->1)
-p( 1--n-)
f:-
ho1,-1
~e.,
J<M'.>I
u OiN
1qfr;,o
or,
(tJO
r{
c.s
;.
p(i~
l-)
2
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