Question

Develop a generator for a random variable whose pdf is
F(x) ={ 1/3, 0<=x<=2
1/24, 2<x<=10
0, otherwise
a) Write a computer routine to generate 1000 values.
b) Plot a histogram of 1000 generated values.
c) Perform goodness-of-fit test to determine whether these generated values fits the theoretical density function given above.
Note: Invlude your computer routine for generating random variates in your answer sheet.

I need numerical solution

Answer 1

A.
gen_obs <- function(){ u1 runif(1) if(u1 <= 2/3){ 2*runif(1) return(u) u = } else{ u = 2 + 8*runif(1) return(u) } نها obs replicate(1000, gen_obs()) ## Plotting histogram p1 hist(obs, breaks=5, include. lowest=FALSE, right=FALSE) <- ## Chisquare goodness of fir test ## Null Probabilities are obtained by integrating the density within that interval chisq_test <- chisq.test(p1$counts, p = chisq_test C(2/3, 1/12, 1/12, 1/12, 1/12))
B.
Histogram of obs 009 500 400 Frequency 300 200 100 0 0 4 9 oo 10 N obs
C.
ChiSquare goodness of fit test -- We divided into 5 bins and null probabilities are obtained by integrating within the interval Chi-squared test for given probabilities data: p1$counts X-squared - 3.158, df - 4, p-value - 0.5317 Since p value = 0.5317, hence the hypothesis is accepted