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Probability distributions using R Experiment :1 Binomial Distribution Experiment :2 Poisson Distribution Experiment :3 Normal Distribution

  #Lab-8 #Program 1 Probability distribution b1=pbinom( 4 , 12 , 0.2 )   #n=12 p=0.2 b2=dbinom( 3 , 12 , 0.2 ) b3=sum(dbinom( 2 : 4 , 12 , 0.2 )) b4=rbinom( 3 , 12 , 0.2 ) b5= 1 -pbinom( 3 , 12 , 0.2 ) b6= 1 -pbinom( 5 , 12 , 0.2 ) b7=sum(dbinom( 0 : 6 , 12 , 0.2 )) b1 b2 b3 b4 b5 b6 b7 #Program 2 #n=6 #p=0.5 b1=dbinom( 2 , 6 , 0.5 ) b2= 1 -pbinom( 4 , 6 , 0.5 ) b3= 1 -pbinom( 0 , 6 , 0.5 ) b1 b2 b3 #Poisson Distribution #Program 1 n= 2000 p= 0.001 dpois( 3 ,lambda=n*p) ppois( 2 ,lambda=n*p,lower= FALSE ) #Program 2 ppois( 17 ,lambda = 12 ) #Left Tailed #Other Program ppois( 17 ,lambda = 12 ,lower= FALSE ) #Right Tailed #Program 3 ppois( 2 ,lambda = 4 ) #Left Tailed dpois( 3 ,lambda= 4 ) #Normal Distribution #dnorm Ex-1 dnorm( 0 ,mean= 0 ,sd= 1 ) #Ex-2 z_scores=seq(- 3 , 3 ,by= 0.1 ) dvalues=dnorm(z_scores) dvalues #pnorm EX-1 pnorm( 0 ) #EX-2 pnorm( 2 ,mean = 5 ,sd= 3 ,lower.tail = F) #EX-3 1 -pnorm( 2 ,mean = 5 ,sd= 3 ,lower.tail = FALSE ) #qnorm #EX-1 qnorm( 0.5 ) #EX-2 qno...
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Lines of Regression, Angle between two lines of regression and estimated values of variables. Experiment :1 Finding (a) Regression line of y on x and (b) Regression line of x on y. Experiment :2 Predicting y value for a given x. Experiment :3 Angle between two lines of regression

  #Lines of Regression a) x=c( 14 , 19 , 24 , 21 , 26 , 22 , 15 , 20 , 19 ) y=c( 31 , 36 , 48 , 37 , 50 , 45 , 33 , 41 , 39 ) relation=lm(y ~ x) print(relation) #Lines of Regression 2 x=c( 14 , 19 , 24 , 21 , 26 , 22 , 15 , 20 , 19 ) y=c( 31 , 36 , 48 , 37 , 50 , 45 , 33 , 41 , 39 ) relation1=lm(x ~ y) print(relation1) #2)Prediction y values for x x =c( 151 , 174 , 138 , 186 , 128 , 136 , 179 , 163 , 152 , 131 ) y =c( 63 , 81 , 56 , 91 , 47 , 57 , 76 , 72 , 62 , 48 ) relation= lm(y ~ x) a = data.frame(x= 170 ) result = predict(relation,a) print(result) #3) Angle Between Two Lines of regression x=c( 14 , 19 , 24 , 21 , 26 , 22 , 15 , 20 , 19 ) y=c( 31 , 36 , 48 , 37 , 50 , 45 , 33 , 41 , 39 ) r1=lm(y ~ x) r2=lm(x ~ y) m1=r1 $ coeff[ 2 ] m2= 1 /r2 $ coeff[ 2 ] angle=atan((m2-m1)/( 1 +m1*m2))* 180 /pi abs(angle) #Student Task 1 x=c( 1 , 3 , 4 , 6 , 8 , 9 , 11 , 14 ) y=c( 1 , 2 , 4 , 4 , 5 , 7 , 8 , 9 ) print(lm(y ~ x)) print(lm(x ~ y)) #Predict() x =c( 12 , 14 , 32 , 65 , 21 ) y =c( 2...
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