1
Trial-action of exercising the Re time Bernoulli Trials outcome 51 03 Ex) Prob
Binary
one -
.
,
Outcome -
Observed result from 1 trial
P(38)
Sample Space -
Set
containing all possible outcomes
Event -
Subset of
outcomes from sample space P(1) =
p + P(0) = 1 -
p =
2
Ex) Prob
Mutually exclusive outcomes
no
Ex) find prob of getting for K
·
indept Trials
incommon
4
-
↳ P(AUB) P(A + B) = =
P(A) + P(B)
. Kane's = 0
, ,
1 2 3
,
4
independent E Prob o
,
P(s) 1 ALB > A+ B A lB > AB F(1) ? outcomes all
=
are
-
= =
·
P(A)10
"0GB
Y
20 P(u) =
·
1000 3
4 outcomes
PRP Prob
that can
Indep .
Events -> not
affected from previous events (coin toss oo 01 give
Prob *
= P 2 [E =
Pq3
(2) &
.
waysanthappen
.
P
= PAB) PAP(B)
p(2i p
=
Check : =
PAB) =
same
for other 3 possibilities a
: total P(1) = 4 Pg3 P(3) =
(j) p3q Ex) full h
(4)p"go
1
↳
(4)p'q4 P(4)
-
Cross Prod IdiffRE combined into I RE 3
kind
=
Space >
-
.
(fixed #trials) Lof Kind
die Whenairde
s
E
rolling &
36 outcomes Binomial Prob Funct, .
2
=
1 -
p
↳ from I die
(4)p"gn
S
1
from
other die
B(n p)
-
↳
k =
Ex)
-
I
Cand Prob -prob that event B know event A
, , 30
.
has occurred
. , occurs
given we
already
P(Bgiven A) P(BIA) P(B1A) P(BA) Puery small , n
very large
-
>
up = const P(diffb-da
Ex)
=
365 !
=
= =
P(A) P(A)
(365-
G
P(BA) = P(B1A) = Binary read incorrectly 10 for 4 GB of data
P(BIA)P(A) 365
2
Odds of 1 errors
0 ?
P(B1 = Poisson Prob Function la
,
SWWt
,
P(BIA)
Exi)
=
A :
.
B =
EW P(BA) P(() t=
np (59)(4x109) 4 estimate how many times
-
=
ev =
=
an
P(A) =
3(t) =
Ex27 If two events are
mutually exclusive ? K Prob P(1) =
(i) pig- -G
O
%
zero bla if A B did not
Ex) of
accused
1000 cell site
Ex3)
users
av
If two events are independent ? e
,
I
Prob of cell tower 5000
-middr
ed effec e
·
4
2
n = 1000 users
to find P(K
Used to Y calls
/day /user
=
.
, = 4000
cand .
prob of event A when event B has
already occurred.
X
calls/day
- =
day
P(AB) = P(AIB) P(B) =
P(BIA) P(A) Os ,
or Is, In
↳ PLAIB) P(BIA)P(A) Os Ir Is Or The Random Variable
mapp
-
=
, ,
P(B)
wo
Ex) given POIOs=PCIrIIs% = 0 8
.
Os
0 9
1-0
.
9
.
or
F(W) =
%6 -> each
map line
S
find P(1s/Ir) : 1- 0 8 = 0 2
.
0 1
.
0 910 9 .
=
0 1
.
/
:
Prob is 16
Is
. .
P([i)
r
=
"G
P(1s(r) = P(Ir/Is)P(is) ↑ (1r) =
P(Ir/1s)iP(1s) + P(Ir(Os) Plos) P(# b(w(25)
P(Ir) =
0 9(0 2). .
+ 0 . 1(0 8) .
= +t
0
902) 0 26
=
=
.
= 0 6 .
.
PlIc-4) = 0
CDF - prob that X v
Permutations (Order Matters) #of ways objects
.
n can be placed in Ex(x) = P(XIX) randomlies
-
a
I slots wo replacement & we to order (n 1)
regard =
Ex) ↳ sided die each SickeP(D)
EA B Ch slots
objects , ,
Prob (where (0)
=
A, B B, A C A x = 0
p
,
=
C A C , B C
,
C
,
B P(1 001) .
= "c
Plvalue f range) = -t =
Trial-action of exercising the Re time Bernoulli Trials outcome 51 03 Ex) Prob
Binary
one -
.
,
Outcome -
Observed result from 1 trial
P(38)
Sample Space -
Set
containing all possible outcomes
Event -
Subset of
outcomes from sample space P(1) =
p + P(0) = 1 -
p =
2
Ex) Prob
Mutually exclusive outcomes
no
Ex) find prob of getting for K
·
indept Trials
incommon
4
-
↳ P(AUB) P(A + B) = =
P(A) + P(B)
. Kane's = 0
, ,
1 2 3
,
4
independent E Prob o
,
P(s) 1 ALB > A+ B A lB > AB F(1) ? outcomes all
=
are
-
= =
·
P(A)10
"0GB
Y
20 P(u) =
·
1000 3
4 outcomes
PRP Prob
that can
Indep .
Events -> not
affected from previous events (coin toss oo 01 give
Prob *
= P 2 [E =
Pq3
(2) &
.
waysanthappen
.
P
= PAB) PAP(B)
p(2i p
=
Check : =
PAB) =
same
for other 3 possibilities a
: total P(1) = 4 Pg3 P(3) =
(j) p3q Ex) full h
(4)p"go
1
↳
(4)p'q4 P(4)
-
Cross Prod IdiffRE combined into I RE 3
kind
=
Space >
-
.
(fixed #trials) Lof Kind
die Whenairde
s
E
rolling &
36 outcomes Binomial Prob Funct, .
2
=
1 -
p
↳ from I die
(4)p"gn
S
1
from
other die
B(n p)
-
↳
k =
Ex)
-
I
Cand Prob -prob that event B know event A
, , 30
.
has occurred
. , occurs
given we
already
P(Bgiven A) P(BIA) P(B1A) P(BA) Puery small , n
very large
-
>
up = const P(diffb-da
Ex)
=
365 !
=
= =
P(A) P(A)
(365-
G
P(BA) = P(B1A) = Binary read incorrectly 10 for 4 GB of data
P(BIA)P(A) 365
2
Odds of 1 errors
0 ?
P(B1 = Poisson Prob Function la
,
SWWt
,
P(BIA)
Exi)
=
A :
.
B =
EW P(BA) P(() t=
np (59)(4x109) 4 estimate how many times
-
=
ev =
=
an
P(A) =
3(t) =
Ex27 If two events are
mutually exclusive ? K Prob P(1) =
(i) pig- -G
O
%
zero bla if A B did not
Ex) of
accused
1000 cell site
Ex3)
users
av
If two events are independent ? e
,
I
Prob of cell tower 5000
-middr
ed effec e
·
4
2
n = 1000 users
to find P(K
Used to Y calls
/day /user
=
.
, = 4000
cand .
prob of event A when event B has
already occurred.
X
calls/day
- =
day
P(AB) = P(AIB) P(B) =
P(BIA) P(A) Os ,
or Is, In
↳ PLAIB) P(BIA)P(A) Os Ir Is Or The Random Variable
mapp
-
=
, ,
P(B)
wo
Ex) given POIOs=PCIrIIs% = 0 8
.
Os
0 9
1-0
.
9
.
or
F(W) =
%6 -> each
map line
S
find P(1s/Ir) : 1- 0 8 = 0 2
.
0 1
.
0 910 9 .
=
0 1
.
/
:
Prob is 16
Is
. .
P([i)
r
=
"G
P(1s(r) = P(Ir/Is)P(is) ↑ (1r) =
P(Ir/1s)iP(1s) + P(Ir(Os) Plos) P(# b(w(25)
P(Ir) =
0 9(0 2). .
+ 0 . 1(0 8) .
= +t
0
902) 0 26
=
=
.
= 0 6 .
.
PlIc-4) = 0
CDF - prob that X v
Permutations (Order Matters) #of ways objects
.
n can be placed in Ex(x) = P(XIX) randomlies
-
a
I slots wo replacement & we to order (n 1)
regard =
Ex) ↳ sided die each SickeP(D)
EA B Ch slots
objects , ,
Prob (where (0)
=
A, B B, A C A x = 0
p
,
=
C A C , B C
,
C
,
B P(1 001) .
= "c
Plvalue f range) = -t =
