1. **Problem Statement:** Write an R program to generate four-digit random numbers using the multiplicative congruential method. 2. **Formula and Explanation:** The multiplicative congruential method generates a sequence of pseudo-random numbers using the formula: $$X_{n+1} = (a \times X_n + c) \mod m$$ where: - $X_0$ is the seed or initial value, - $a$ is the multiplier, - $c$ is the increment (for pure multiplicative method, $c=0$), - $m$ is the modulus. 3. **Important Rules:** - The generated numbers $X_n$ will be between $0$ and $m-1$. - To get four-digit numbers, choose $m$ such that $m \leq 10000$. - The seed $X_0$ must be between $0$ and $m-1$. 4. **R Program Explanation:** - The program will prompt the user to input $X_0$, $a$, $c$, and $m$. - It will generate a sequence of random numbers using the formula. - It will print the generated four-digit numbers. 5. **Sample R Code:** ```r # Function to generate n random numbers generate_random <- function(X0, a, c, m, n=10) { X <- numeric(n) X[1] <- X0 for(i in 2:n) { X[i] <- (a * X[i-1] + c) %% m } return(X) } # User inputs cat("Enter seed X0 (0 <= X0 < m): ") X0 <- as.integer(readLines(con = stdin(), n = 1)) cat("Enter multiplier a: ") a <- as.integer(readLines(con = stdin(), n = 1)) cat("Enter increment c: ") c <- as.integer(readLines(con = stdin(), n = 1)) cat("Enter modulus m (<= 10000): ") m <- as.integer(readLines(con = stdin(), n = 1)) # Generate and print random numbers random_numbers <- generate_random(X0, a, c, m, 10) cat("Generated four-digit random numbers:\n") print(random_numbers) ``` This program generates 10 random numbers using the multiplicative congruential method with user inputs. **Final answer:** The above R code fulfills the requirement to generate four-digit random numbers using the multiplicative congruential method.