R Programming examples

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Answers:
Note: the lines starting with hash symbol represent comments. They are not part of the actual codes.
#1
(log(919,2)-3)/log(919,10)-1
#2
#a
y=rchisq(10000,5)
#b
p=y[which(y>2&y<3)]
length(p)
#or in one line
length(y[which(y>2&y<3)])
#c
x=ifelse(y<1,0,ifelse(y>=3,2,1))
#d
mean(y)
median(y)
#e
#we know median of chi-squared dist = k(1-
5*(1-2/(9*5))^2
#3
X=matrix(c(1:14,31:44,61:74),7)
Y=X[4:7,1:4]
solve(Y%*%t(Y))

#4
#a
dpois(2,4)
#b
ppois(2,4)
#c
1-ppois(4,4)
#d
ppois(6,4)-ppois(2,4)
#e
#This is a technique. there may be a better technique
x=0
d=ppois(x,4)
while(d<.5)
  {
   x=x+1
   d=ppois(x,4)
  }
x
#Yes! there is a better technique
qpois(0.5,4)
#5
#(i)
dt(3,5)
#(ii)
pt(3,5)
#(iii)
pt(4,5)
#(iv)
1-pt(6,5)
#v)
pt(1,5)-pt(-2,5)
#(vi)
pt(1,50-pt(-1,5)
#(vii)
qt(.7,5)

#6
#new function to find kurtosis
kurt=function(x)
  {
   mean(x-mean(x))^4/var(x)^2
  }