
    f <- function(x){(x/4)*exp(-x^2/8)}


    # Definir la función ex

    # Calcula el valor esperado de X
 
    # Definir la función ex2
   
    # Calcular la varianza de X


    # Definir la función ex
    ex <- function(x){x*f(x)}

    # Calcula el valor esperado de X
    expected_value <- integrate(ex, 0, Inf)$value

    # Definir la función ex2
    ex2 <- function(x){x^2*f(x)}

    # Calcular la varianza de X
    variance <- integrate(ex2, 0, Inf)$value - expected_value^2


    test_function_definition("ex",
                          function_test = {
                            test_expression_result("ex(1)")
                            test_expression_result("ex(4)")
                            test_expression_result("ex(10)")
                            test_expression_result("ex(100)")
                          })
    test_function("integrate", args = c("f", "lower", "upper"), eval = c(F, T, T)) 
    test_object("expected_value")
    test_function_definition("ex2",
                          function_test = {
                            test_expression_result("ex2(1)")
                            test_expression_result("ex2(4)")
                            test_expression_result("ex2(10)")
                            test_expression_result("ex2(100)")
                          })
    test_function("integrate", args = c("f", "lower", "upper"), eval = c(F, T, T))
    test_object("variance")