curve(dt(x, df = 1), xlim = c(-4, 4)) set.seed(123) # generate 1000 random numbers from the given distribution. Assign them to the variable x. # compute the sample mean of x. set.seed(123) # generate 1000 random numbers from the given distribution. Assign them to the variable x. x <- rt(1000, df = 1) # compute the sample mean of x. mean(x) # Although a t distribution with M = 1 is, as every other t distribution, symmetric around zero it actually has no expectation. This explains the highly non-zero value for the sample mean. test_object("x") test_function_result("mean") success_msg("Well done! The expectation is not defined for a t distributed RV with one degree of freedom: although a t distribution with M = 1 is, as every other t distribution, symmetric around zero it actually has no expectation. This explains the non-zero value of the sample mean.")