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{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "binomial(39,i)/binomial(52,i); # Pr
 that the first i cards contain no spade (hypergeometric)" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#*&-%)binomialG6$\"#R%\"iG\"\"\"-F%6$\"#_F(!\"\"
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "f:=binomial(39,i-1)/binomial
(52,i-1)-%;  #  f(i) = F(i) - F(i-1)" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"fG,&*&-%)binomialG6$\"#R,&%\"iG\"\"\"F-!\"\"F--F(6$\"#_F+F.F-*&-
F(6$F*F,F--F(6$F1F,F.F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "mu:=eva
lf(add(f*i,i=1..40));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+'G9
dy$!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sqrt(add(f*i^2,i
=1..40)-mu^2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#$\"+Q&4K-$!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
2 "Q2" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 
"restart: W:=3*Y-2*X;  # where Y is the number of spades and X the num
ber of dots (independent)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"WG,&*
&\"\"$\"\"\"%\"YGF(F(*&\"\"#F(%\"XGF(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "3*1/4*9-2*7/2.;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!
*+++]#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "sqrt(9*9*1/4.
*3/4*(43/51)+4*35/12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1%**o%\\
!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "P:=(z^(-2)+z^(-4)+z^(-6)+z^
(-8)+z^(-10)+z^(-12))/6.*\nadd(binomial(13,i)*binomial(39,9-i)*z^(3*i)
,i=0..9)/binomial(52,9):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 
"add(coeff(P,z,i),i=7..25);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+(*[
iE5!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "add(coeff(P^5,z,i),i=7..5*
25);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Q<$*>C!#5" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 2 "Q3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 25 "restart:  f:=c*(i^2+j^2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"fG*&%\"cG\"\"\",&*$)%\"iG\"\"#F'F'*$)%\"jGF,F'F'F
'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "add(add(f,j=max(1,i)..2+abs(
i)),i=-1..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"#!)\"\"\"%\"cGF
&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "c:=1/80;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"cG#\"\"\"\"#!)" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 89 "seq(seq([i,j,f],j=max(1,i)..2+abs(i)),i=-1..2);  # \+
make this into table of probabilities:" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6-7%!\"\"\"\"\"#F%\"#S7%F$\"\"##F%\"#;7%F$\"\"$#F%\"\")7%\"\"!F%#F
%\"#!)7%F1F)#F%\"#?7%F%F%F&7%F%F)F*7%F%F-F.7%F)F)#F%\"#57%F)F-#\"#8F37
%F)\"\"%#F%FA" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "b) " }{MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "mx:=add(add(i*f,j=
max(1,i)..2+abs(i)),i=-1..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#mx
G#\"#T\"#S" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "my:=add(add(j
*f,j=max(1,i)..2+abs(i)),i=-1..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%#myG#\"#d\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "add(add(
(i-mx)*(j-my)*f,j=max(1,i)..2+abs(i)),i=-1..2): evalf(%);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#$\"+++]PX!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
43 "g:=[5,4,5,8]: g:=evalm(g/add(g[i],i=1..4));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gG-%'vectorG6#7&#\"\"&\"#A#\"\"#\"#6F)#\"\"%F." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "muX:=-5/22+5/22+2*4/11;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$muXG#\"\")\"#6" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 9 "3*muX-1.;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"+#====\"!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q4" }{MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "restart:  L1:=18.3/12.:  \+
L2:=18.3/6.:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "add(L1^i/i!
,i=0..2)*exp(-L1)-add(L2^i/i!,i=0..2)*exp(-L2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+J\"QY!R!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b
)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "L:=
29/60*18.3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "1-add(L^i/i!
,i=0..6)*exp(-L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+lWL(y(!#5" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "2-3*L; 3*sqrt(L);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#$!+++]`C!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+
;M;A*)!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q5" }{MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "restart: # Pr(X=j) = \+
Sum[Pr(X=j|Y=i),i=j..3) by Total Probability formula (or by\n#   Proba
bility tree), where Y is the number of sixes and X is the number of sp
ades:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "pr:=seq(add(binom
ial(3,i)*5^(3-i)/6.^3*\nbinomial(13,j)*binomial(39,i-j)/binomial(52,i)
,i=j..3),j=0..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#prG6&$\"+![?%)
z)!#5$\"+q\"eP:\"F($\"+BAAAZ!#7$\"+/aG\"*f!#9" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 28 "mu:=add((k-1)*pr[k],k=1..4);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#muG$\"++++]7!#5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "sigma:=sqrt(add((k-1-mu)^2*pr[k],k=1..4));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG$\"+F+B_M!#5" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 37 "add((k-1-mu)^3*pr[k],k=1..4)/sigma^3;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+(RM!GE!\"*" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 37 "add((k-1-mu)^4*pr[k],k=1..4)/sigma^4;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+f?,u\"*!\"*" }}}}{MARK "48" 0 }
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