#plotting the random variables and probability values
col <- rainbow(4)
a <- c(1,2,5,10)
plot(0,0,main="Probability density graph",xlab="Random variable",ylab="Probability density values",
xlim = c(0,1),ylim = c(0,4))
for (i in 1:4)
{
lines(seq(0,1,by=0.01),dGAMMA(seq(0,1,by=0.01),a[i],a[i])$pdf,col = col[i])
}
dGAMMA(seq(0,1,by=0.01),5,6)$pdf #extracting the pdf values
dGAMMA(seq(0,1,by=0.01),5,6)$mean #extracting the mean
dGAMMA(seq(0,1,by=0.01),5,6)$var #extracting the variance
#plotting the random variables and cumulative probability values
col <- rainbow(4)
a <- c(1,2,5,10)
plot(0,0,main="Cumulative density graph",xlab="Random variable",ylab="Cumulative density values",
xlim = c(0,1),ylim = c(0,1))
for (i in 1:4)
{
lines(seq(0,1,by=0.01),pGAMMA(seq(0,1,by=0.01),a[i],a[i]),col = col[i])
}
pGAMMA(seq(0,1,by=0.01),5,6) #acquiring the cumulative probability values
mazGAMMA(1.4,5,6) #acquiring the moment about zero values
mazGAMMA(2,5,6)-mazGAMMA(1,5,6)^2 #acquiring the variance for a=5,b=6
#only the integer value of moments is taken here because moments cannot be decimal
mazGAMMA(1.9,5.5,6)
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