# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 
# set output 'prob.7.png'
set format x "%2.0f" 
set format y "%3.2f" 
set key fixed left top vertical Right noreverse enhanced autotitle box lt black linewidth 1.000 dashtype solid
unset key
set samples 30, 30
set style data lines
set ytics  norangelimit 0.00000,0.0239117 ,0.239117
set title "binomial PDF with n = 25, p = 0.15" 
set trange [ -1.00000 : 1.00000 ] noreverse nowriteback
set urange [ * : * ] noreverse nowriteback
set vrange [ * : * ] noreverse nowriteback
set xlabel "k" 
set xrange [ -2.00000 : 27.0000 ] noreverse nowriteback
set x2range [ * : * ] noreverse writeback
set ylabel "probability density" 
set yrange [ 0.00000 : 0.239117 ] noreverse nowriteback
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set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
isint(x)=(int(x)==x)
Binv(p,q)=exp(lgamma(p+q)-lgamma(p)-lgamma(q))
arcsin(x,r)=r<=0?1/0:abs(x)>r?0.0:invpi/sqrt(r*r-x*x)
beta(x,p,q)=p<=0||q<=0?1/0:x<0||x>1?0.0:Binv(p,q)*x**(p-1.0)*(1.0-x)**(q-1.0)
binom(x,n,p)=p<0.0||p>1.0||n<0||!isint(n)?1/0:  !isint(x)?1/0:x<0||x>n?0.0:exp(lgamma(n+1)-lgamma(n-x+1)-lgamma(x+1)  +x*log(p)+(n-x)*log(1.0-p))
cauchy(x,a,b)=b<=0?1/0:b/(pi*(b*b+(x-a)**2))
chisq(x,k)=k<=0||!isint(k)?1/0:  x<=0?0.0:exp((0.5*k-1.0)*log(x)-0.5*x-lgamma(0.5*k)-k*0.5*log2)
erlang(x,n,lambda)=n<=0||!isint(n)||lambda<=0?1/0:  x<0?0.0:x==0?(n==1?real(lambda):0.0):exp(n*log(lambda)+(n-1.0)*log(x)-lgamma(n)-lambda*x)
extreme(x,mu,alpha)=alpha<=0?1/0:alpha*(exp(-alpha*(x-mu)-exp(-alpha*(x-mu))))
f(x,d1,d2)=d1<=0||!isint(d1)||d2<=0||!isint(d2)?1/0:  Binv(0.5*d1,0.5*d2)*(real(d1)/d2)**(0.5*d1)*x**(0.5*d1-1.0)/(1.0+(real(d1)/d2)*x)**(0.5*(d1+d2))
gmm(x,rho,lambda)=rho<=0||lambda<=0?1/0:  x<0?0.0:x==0?(rho>1?0.0:rho==1?real(lambda):1/0):  exp(rho*log(lambda)+(rho-1.0)*log(x)-lgamma(rho)-lambda*x)
geometric(x,p)=p<=0||p>1?1/0:  !isint(x)?1/0:x<0||p==1?(x==0?1.0:0.0):exp(log(p)+x*log(1.0-p))
halfnormal(x,sigma)=sigma<=0?1/0:x<0?0.0:sqrt2invpi/sigma*exp(-0.5*(x/sigma)**2)
hypgeo(x,N,C,d)=N<0||!isint(N)||C<0||C>N||!isint(C)||d<0||d>N||!isint(d)?1/0:  !isint(x)?1/0:x>d||x>C||x<0||x<d-(N-C)?0.0:exp(lgamma(C+1)-lgamma(C-x+1)-lgamma(x+1)+  lgamma(N-C+1)-lgamma(d-x+1)-lgamma(N-C-d+x+1)+lgamma(N-d+1)+lgamma(d+1)-lgamma(N+1))
laplace(x,mu,b)=b<=0?1/0:0.5/b*exp(-abs(x-mu)/b)
logistic(x,a,lambda)=lambda<=0?1/0:lambda*exp(-lambda*(x-a))/(1.0+exp(-lambda*(x-a)))**2
lognormal(x,mu,sigma)=sigma<=0?1/0:  x<0?0.0:invsqrt2pi/sigma/x*exp(-0.5*((log(x)-mu)/sigma)**2)
maxwell(x,a)=a<=0?1/0:x<0?0.0:fourinvsqrtpi*a**3*x*x*exp(-a*a*x*x)
negbin(x,r,p)=r<=0||!isint(r)||p<=0||p>1?1/0:  !isint(x)?1/0:x<0?0.0:p==1?(x==0?1.0:0.0):exp(lgamma(r+x)-lgamma(r)-lgamma(x+1)+  r*log(p)+x*log(1.0-p))
nexp(x,lambda)=lambda<=0?1/0:x<0?0.0:lambda*exp(-lambda*x)
normal(x,mu,sigma)=sigma<=0?1/0:invsqrt2pi/sigma*exp(-0.5*((x-mu)/sigma)**2)
pareto(x,a,b)=a<=0||b<0||!isint(b)?1/0:x<a?0:real(b)/x*(real(a)/x)**b
poisson(x,mu)=mu<=0?1/0:!isint(x)?1/0:x<0?0.0:exp(x*log(mu)-lgamma(x+1)-mu)
rayleigh(x,lambda)=lambda<=0?1/0:x<0?0.0:lambda*2.0*x*exp(-lambda*x*x)
sine(x,f,a)=a<=0?1/0:  x<0||x>=a?0.0:f==0?1.0/a:2.0/a*sin(f*pi*x/a)**2/(1-sin(twopi*f))
t(x,nu)=nu<0||!isint(nu)?1/0:  Binv(0.5*nu,0.5)/sqrt(nu)*(1+real(x*x)/nu)**(-0.5*(nu+1.0))
triangular(x,m,g)=g<=0?1/0:x<m-g||x>=m+g?0.0:1.0/g-abs(x-m)/real(g*g)
uniform(x,a,b)=x<(a<b?a:b)||x>=(a>b?a:b)?0.0:1.0/abs(b-a)
weibull(x,a,lambda)=a<=0||lambda<=0?1/0:  x<0?0.0:x==0?(a>1?0.0:a==1?real(lambda):1/0):  exp(log(a)+a*log(lambda)+(a-1)*log(x)-(lambda*x)**a)
carcsin(x,r)=r<=0?1/0:x<-r?0.0:x>r?1.0:0.5+invpi*asin(x/r)
cbeta(x,p,q)=ibeta(p,q,x)
cbinom(x,n,p)=p<0.0||p>1.0||n<0||!isint(n)?1/0:  !isint(x)?1/0:x<0?0.0:x>=n?1.0:ibeta(n-x,x+1.0,1.0-p)
ccauchy(x,a,b)=b<=0?1/0:0.5+invpi*atan((x-a)/b)
cchisq(x,k)=k<=0||!isint(k)?1/0:x<0?0.0:igamma(0.5*k,0.5*x)
cerlang(x,n,lambda)=n<=0||!isint(n)||lambda<=0?1/0:x<0?0.0:igamma(n,lambda*x)
cextreme(x,mu,alpha)=alpha<=0?1/0:exp(-exp(-alpha*(x-mu)))
cf(x,d1,d2)=d1<=0||!isint(d1)||d2<=0||!isint(d2)?1/0:1.0-ibeta(0.5*d2,0.5*d1,d2/(d2+d1*x))
cgmm(x,rho,lambda)=rho<=0||lambda<=0?1/0:x<0?0.0:igamma(rho,x*lambda)
cgeometric(x,p)=p<=0||p>1?1/0:  !isint(x)?1/0:x<0||p==0?0.0:p==1?1.0:1.0-exp((x+1)*log(1.0-p))
chalfnormal(x,sigma)=sigma<=0?1/0:x<0?0.0:erf(x/sigma/sqrt2)
chypgeo(x,N,C,d)=N<0||!isint(N)||C<0||C>N||!isint(C)||d<0||d>N||!isint(d)?1/0:  !isint(x)?1/0:x<0||x<d-(N-C)?0.0:x>d||x>C?1.0:hypgeo(x,N,C,d)+chypgeo(x-1,N,C,d)
claplace(x,mu,b)=b<=0?1/0:(x<mu)?0.5*exp((x-mu)/b):1.0-0.5*exp(-(x-mu)/b)
clogistic(x,a,lambda)=lambda<=0?1/0:1.0/(1+exp(-lambda*(x-a)))
clognormal(x,mu,sigma)=sigma<=0?1/0:x<=0?0.0:cnormal(log(x),mu,sigma)
cnormal(x,mu,sigma)=sigma<=0?1/0:0.5+0.5*erf((x-mu)/sigma/sqrt2)
cmaxwell(x,a)=a<=0?1/0:x<0?0.0:igamma(1.5,a*a*x*x)
cnegbin(x,r,p)=r<=0||!isint(r)||p<=0||p>1?1/0:  !isint(x)?1/0:x<0?0.0:ibeta(r,x+1,p)
cnexp(x,lambda)=lambda<=0?1/0:x<0?0.0:1-exp(-lambda*x)
cpareto(x,a,b)=a<=0||b<0||!isint(b)?1/0:x<a?0.0:1.0-(real(a)/x)**b
cpoisson(x,mu)=mu<=0?1/0:!isint(x)?1/0:x<0?0.0:1-igamma(x+1.0,mu)
crayleigh(x,lambda)=lambda<=0?1/0:x<0?0.0:1.0-exp(-lambda*x*x)
csine(x,f,a)=a<=0?1/0:  x<0?0.0:x>a?1.0:f==0?real(x)/a:(real(x)/a-sin(f*twopi*x/a)/(f*twopi))/(1.0-sin(twopi*f)/(twopi*f))
ct(x,nu)=nu<0||!isint(nu)?1/0:0.5+0.5*sgn(x)*(1-ibeta(0.5*nu,0.5,nu/(nu+x*x)))
ctriangular(x,m,g)=g<=0?1/0:  x<m-g?0.0:x>=m+g?1.0:0.5+real(x-m)/g-(x-m)*abs(x-m)/(2.0*g*g)
cuniform(x,a,b)=x<(a<b?a:b)?0.0:x>=(a>b?a:b)?1.0:real(x-a)/(b-a)
cweibull(x,a,lambda)=a<=0||lambda<=0?1/0:x<0?0.0:1.0-exp(-(lambda*x)**a)
gsampfunc(t,n) = t<0?0.5*1/(-t+1.0)**n:1.0-0.5*1/(t+1.0)**n
NO_ANIMATION = 1
fourinvsqrtpi = 2.25675833419103
invpi = 0.318309886183791
invsqrt2pi = 0.398942280401433
log2 = 0.693147180559945
sqrt2 = 1.4142135623731
sqrt2invpi = 0.797884560802865
twopi = 6.28318530717959
save_encoding = "utf8"
eps = 1e-10
xmin = -2
xmax = 27
ymin = -5
ymax = 0.239117116019606
r = 2.0
mu = 3.75
sigma = 1.78535710713571
p = 0.15
q = 3.0
n = 25
plot binom(x, n, p) with impulses