Question

*has to with R program, I need the code for R script*

I already have questions 1 through solved and posted a picture of them. I need help with questions 4-11 please!!! thank u

4 plots a histogram showing the distribution of your X. 5 generates a data series Y with a length equal to 'howmany' 6 plots the distribution Y 7 assigns the series X to a new variable Z. 8 calculates the variance of the series Z using a formula that you construct that cannot involve the R functions var() or sd). (This will show that you can write a formula to calculate variance). 9 calculates the difference between variance you calculated for the series Z using the formula that you constructed and the variance calculated by the R functions var(). 10 calculates the variance of the series Y using the formula that you constructed. 11 plots Y against X. Extra mark will be given for good labelling and use of color.

Answer 1

define how many howmany <- 182 Data series x with length equal to "howmany" and a non normal but random distribution. ### Creating a uniform distribuiton xl <- runif (60,min=1,max=50) ### Generating a poission distribution x2 <- rpois (n=60, lambda =4 ) ### Generationg a exponential distribuiton x3 <- rexp (n=62, rate = 3.9) ### combining the 3 vectors X <- c(x1, x2, x3) 4. Histogram of X hist(X)

Histogram of X 100 80 60 Frequency 40 20 10 1 20 30 40 50 5. Data series Y with length equal to howmany ### creating chisqure distribu yl <- rchisa (n=122,100) ### creating a log normal distrbution y2 <- rlnorm (30, meanlog = 0.01, sdlog = 0.22) ### creating a expotential distribution y3 <- rexp (n=30, rate = 1) ### combining the vectors Y <- c(yl, y2, y3)

6.Plot the distribution of Y hist (Y) Histogram of Y 60 50 40 Frequency 30 20 10 0 50 100 150 7 Assign X to new variable z z <- X

8 Calcuate the variance in Z cal_var <- function () { n <- length (v) ## length of v sum_v <- sum (v) *** sum of v mean_v <- sum v/n ### mean of v SS_V <- sum((v-mean_v)^2) ### sum of square of the difference of each v with the mean. var_v <- 33_v/ (n-1)} var_z<- cal_var (2) 9. Difference in variance. var_z -var (2) ## [1] 0 10 Variance of Y var_y <- cal_var (Y) 11.Plot Y against X plot (x = x, y = Y, xlab = "X", ylab="Y", main = "Plot of Y against X" )

0 20 40 60 80 100 140 IIIIIIII OP 00000 0008 oo 0 O oo 00 OO 0 0000 90 0 0 | 0 10 0° 800 08 0 0 20 Plot of Y against X O 30 40 Oo 50