Question

Question 4(4 point)

4.1) Which of the following produces a probability histogram?

1. Hist(1:1000, probability=TRUE) ,
2. histogram(1:1000, probability=TRUE)
3. hist(rexp(1000,3))
4. hist(rbinom(1000, 10, 0.2))
5. Noe of these

4.2) Which of the following R code generates 1000 random variates from an Exponential distribution with mean 1/3?

1. rexp(1000, rate=1/3)
2. rexp(1/3, 1000)
3. rexp(1000, rate=3)
4. rexp(3, 1000)
5. None of these

4.3) Which of the following R code generates 1000 random variates from a Normal distribution with mean 10 and variance 4?

1. rnorm(1000, 10, 4)
2. rnorm(1000, 4, 10)
3. rnorm(10, 4, 1000)
4. rnorm(1000, 10, 2)
5. rnorm(10, 2, 1000)

4.4) Which of the following R code generates 1000 random variates from an Exponential distribution with mean 1/3?

1. 3*log(1-runif(1000))
2. log(1-runif(1000))/3
3. -log(1-runif(1000))/3
4. -3*log(1-runif(1000))
5. None of these

Answer 1

4.1) Which of the following produces a probability histogram?

A probability histogram is a graph that shows the probability of each outcome on axis.

C. hist(rexp(1000,3))

4.2) Which of the following R code generates 1000 random variates from an Exponential distribution with mean 1/3?

In R “rate” is what we call Lambda.

Lambda = .2 So, mean = sd = 1/.2

hence here mean = sd = 1/3  so, Lambda = 3

C. rexp(1000, rate=3)

4.3) Which of the following R code generates 1000 random variates from a Normal distribution with mean 10 and variance 4?

rnorm(n, mean = 0, sd = 1)

Here, variance is 4 hence standard deviation is 2.

D. rnorm(1000, 10, 2)

4.4) Which of the following R code generates 1000 random variates from an Exponential distribution with mean 1/3?

For exponential distribution we use rexp.

E. None of these