5. Performing Statistics R- II

 5. Performing Statistics R- II

 5) Write an R program to implement time series analysis for the given data

CODE:

OUTPUT :

 5B) Write an R program to implement.

i) Normal Distribution. [Hint: dnorm(), pnorm(), qnorm(), rnorm()] 

ii) Binomial Distribution. [Hint: dbinom(), pbinom(), qbinom(), rbinom()]

CODE:

# Normal Distribution
set.seed(123)  # Set seed for reproducibility

# Parameters for the normal distribution
mean_value <- 0
sd_value <- 1

# Generate random samples from a normal distribution
random_samples <- rnorm(1000, mean = mean_value, sd = sd_value)

# Calculate probability density function (PDF) at specific points
pdf_values <- dnorm(random_samples, mean = mean_value, sd = sd_value)

# Calculate cumulative distribution function (CDF) at specific points
cdf_values <- pnorm(random_samples, mean = mean_value, sd = sd_value)

# Quantile function (inverse CDF) - Find the value corresponding to a given probability
quantile_value <- qnorm(0.95, mean = mean_value, sd = sd_value)

cat("Normal Distribution:\n")
cat("Quantile (Inverse CDF) at probability 0.95:", quantile_value, "\n\n")

# Binomial Distribution
# Parameters for the binomial distribution
n_trials <- 10
prob_success <- 0.5

# Generate random samples from a binomial distribution
binom_samples <- rbinom(1000, size = n_trials, prob = prob_success)

# Calculate probability mass function (PMF) at specific points
pmf_values <- dbinom(binom_samples, size = n_trials, prob = prob_success)

# Calculate cumulative distribution function (CDF) at specific points
cdf_binom_values <- pbinom(binom_samples, size = n_trials, prob = prob_success)

# Quantile function (inverse CDF) - Find the value corresponding to a given probability
quantile_binom_value <- qbinom(0.95, size = n_trials, prob = prob_success)

cat("Binomial Distribution:\n")
cat("Quantile (Inverse CDF) at probability 0.95:", quantile_binom_value, "\n")

    

OUTPUT :

Normal Distribution:
Quantile (Inverse CDF) at probability 0.95: 1.644854 

Binomial Distribution:
Quantile (Inverse CDF) at probability 0.95: 8