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tk4Solution: STAT400 - sp 20
①Ha Khanh Nguyen
(a) X = # of Kahuna in 10 Pokemon
X N Bi nom ( n - IQ. p = 0.35)I ( X S, l) = I - I (X Ll) = I - I ( X = O)
= I - ( Y ) (O. 35J ( l - O .35)"=
'
0.98650
( b) X = # of type Bug in 10 Pokemon
X - Binom ( n = 10, p = 0.05 t O.
05 t O. 5 t O. 35 = 0.95)
IC X 77) = E ( X 3 8) = I - I ( X 's 8) = I - I ( X SF)
= I - 0.0115 = 0.98850T R : pbinom ( 7, 10, 0.95) or cdf table
→ geometric(c) X = # of Pokemon you see until your 1st Ini Kachur
gR defines thisas # of failuresX ~ Geom ( p = 0.05) f- R : pgeom (7 , 0.05) before 1st
IC X > 8) = I - I ( X f 8) = I - O.3366 = ( not #hf%§
OR = I ( X 79) = ×¥a ( I - 0.05)" '( 0.05)
= 0.05¥5 ( 0.95 ) "n
05 ⇐g 0.95" = 0.05×1%9.5/7= 0.66340
(d) X = # of Pokemon you see until the 3rd Pikachu
X ~ Neg Binom ( k =3, p = 0.05)
I ( X = lo) = ( 103? ) 0.053 ( I - 0.05)" - 3
= ( 92) 0.05 ' (0.9577=0.003140①
(e) Xp , X w , X µ N Multibinom (n -- 10 , pie = 0.05, pw= 0.5, pk -- 0.35)10 !
I ( Xp = 2, X w =3, Xk = 5) =s! ( 0.05)-
(0.5)'
( 0.3535
= 0.004136T
② I ( Metapod / Red) ⇐ 0.05 I ( Metapod / Blue) = 0.35
I ( Red) = I ( Blue) = 0.5
X = # of Metapods encountered ,X - Binom (n -- 20 , p = f
0.05 if play Red
We want : I ( Red / x = 4)0.35 tf play Blue
)
But we have : I ( X = 41 Red) = ( 240 ) 0.054 ( I - 0.05)"I ( X = 41 Blue) = ( 240 ) 0.354 ( I - 0.35)
"
By Bayes'Rule
,
I ( x -- 41 Red) I ( Red)I ( Red l X -- 4) =-
I ( X -- 41 Red) I ( Red) t IC X = 41 Blue) IC Bluet= ((240100540.951%6.5)-4240)0.054 0.95 "]. (O
. 5) t ( (Y) o .3540.65' ']I5)
= 0.15290
②
③ X = # of encounters in lo stepsX - Poisson ( d = I
. 5)
(a) I ( X 32) ⇐ I - I ( X -
- O) - I (x =D= I - d°oe - d',e = I -
I.5°e5 - h51!= 0.44422T
(b) Y = # of encounters in 15 stepsD= 1.5 for 10 steps
Y - Poisson ( D= 2.25)D= ( ) Is for 15 steps
= 2.25ICY f 5)
= I ( Y = O) t I ( Y =L) t IC 4=2) t ICY =3) t I ( Y - 4) t I ( y = 5)
= d°g t "t'e t "e t "7 t *e= 0.97260
OR I C y f5) = I - ICY > 5) = I - I ( Y > G)
= I - FI. '" = I - e-''E. '÷
net '÷ . '÷.÷±÷÷÷÷¥÷ ,= I - e- '
' Ce " - I - d - II - II - II - IIT)= 0.97260
③
④(a) X = # of Flying Pokemon
X - Hypergeometric ( N -- 19
,K -- 3
,n-- G )
ecx =p .(7)( 'II )
= YET = 0.482970OR
19
s!'
isgthers "YI-
- IFT - 0.482970
If we assume (3) ( if) IT #ftoYder9's Pokemonorder matters
, ¥= 13526-3=0.48297
(b) Y = # of Psychic PokemonY - Hypergeometric ( N = 19
,K -- 6
, n= G)
ICY f 4) = I - Ily = 5) - ICY -- G)-
- i. lEY;g- -
l:Yi!j=a④OR 19 191
6¥ 43 others 6¥ 43 others same answer
T T T t
5 I G O
"www.amsafffs,
i - lEH7 -
(8) (9) a.1916 1¥
= 0.9971
④
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