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