Question

R programming Language Problem

1. Create three vectors, each containing 20 values randomly sampled from a normal distribution. The first should be from a normal distribution with mean = 0 and standard deviation = 1 (a.k.a. the standard normal distribution). The second should be from a normal distribution with mean = 10 and standard deviation = 1. The third should be from a normal distribution with mean = 10 and standard deviation = 10.

Use the mean() and sd() functions in R to check the means and standard deviations for each of your three vectors. Why don’t these have the exact same means and standard deviations as the distributions used to generate them? Do their means and standard deviations seem reasonable anyway? (For this problem, please have R display the values in all three vectors along with their means and standard deviations.)

2. For this problem, you will use R to simulate flipping a coin 25 times. Create a vector that contains two values, one for “heads” and one for “tails”. Then use the sample() function to randomly choose one of the two values in this vector, 25 times.

Answer 1

1)

We create three vectors with 20 values each from the normal distribution using rnorm function. Then calculate the means and standard deviation and print them.

The output:

The observed means and standard deviations aren't the exact same as the actual values. This is because we have sampled only 20 values from the normal distributions hence there is some amount of error introduced when we compute the means and std from the vectors. Increasing the number of values sampled to a much higher number should reduce the error observed

R Code.

a = rnorm(20, mean=0, sd=1)
b = rnorm(20, mean=10, sd=1)
c = rnorm(20, mean=10, sd=10)

mean_a = mean(a)
sd_a = sd(a)
mean_b = mean(b)
sd_b = sd(b)
mean_c = mean(c)
sd_c = sd(c)

print(paste("Mean, standard deviation of 1st vector: ", toString(mean_a), toString(sd_a)))
print(paste("Mean, standard deviation of 2nd vector: ", toString(mean_b), toString(sd_b)))
print(paste("Mean, standard deviation of 3rd vector: ", toString(mean_c), toString(sd_c)))

2) We simulate the coin flip 25 times using a binomial distribution. Use the rbinom() function to do so. It takes 3 arguments, 1st is the number of flips which is 25, then is the number of coins flipped which is 1, and the final one is probability of gettings heads which is 0.5 (assuming unbiased coin).

Then use the sample function, pass the coin vector and size as 25 to sample values 25 times.

Output

R Code

coins = rbinom(25, 1, 0.5)
print(coins)
print(sample(coins, size=25))