Question

6. Estimate expr)dx by generating random numbers. Generate at least 100 values and stop when the standard deviation of your estimator is less than 0.01. 12. To estimate θ, we generated 20 independent values having mean θ. If the successive values obtained were 102. 112. 131, 107, 114. 95, 133, 145, 139, 117 93. 111, 124, 122, 136, 141, 119. 122, 151, 143 how many additional random variables do you think we will have to generate if we want to be 99 percent certain that our final estimate of θ is correct to within +0.5? 15. If n 15 and the data are 5, 4, 9. 6, 21, 17. 11, 20. 7, 10,21, 15, 13, 16, 8 approximate (by a simulation) the bootstrap estimate of Var(S).

can u solve those 3 questions and in R program as well ?

Answer 1

The R code for finding the definite integral using Mote Carlo Simulation is given below. We generate uniform random numbers between 0 and 1 starting with $N=100$ . The iteration stops when the standard deviation is less than 0.01.

g <- function (x)
{
gg <- exp(x^2)
return (gg)
}
N < - 100
While (sd > 0.01)
{
I <- 0
I2 <- 0
X <- runif(N)
for(i in 1:N)
{
  
I <- I + g(X[i])/N
I2 <- I2 + g(X[i])^2/N
}
sd <- sqrt((I2-I^2)/N)
N <- N + 1
}
N
I

The simulated value is  1.461569. While the exactt value is 1.46265.

We are required to solve only one question. Please post the remaining questions as another post.