Using R,

Exercise 1 (Working with Vectors) Recall the definitions of sample mean and sample standard deviation for data r1, r2, .. .In Consider the following vector of data. x-c(1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144) (a) Calculate the sample mean of x without the use of mean ), sd(), sum ), or t. Hint: Recall that vectors in R are column vectors. (Although when you display them, they often look like row vectors.) You may need to create a second vector, which is allowed, and should also look into the function crossprod). Essentially you need to use matrix algebra to recreate the formulas above. You may use mean ) to check your answer (b) Calculate the sample standard deviation of x without the use of mean), sd(), sum ), or +. You may use sdO to check your