Question 2. (4 marks). The generalised mean {with exponent is? > U) of a random variable X is dened as: (we)? where E (X k} is the expected value of X k. The generalised mean generalises several measures of centralit}r into one (for example, if I: = 1, then the usual expected value is obtained). (a) \"trite code for an R function generalisedaean which takes as input three variables: events. probabilities and k, and returns the generalised mean with exponent is (as per the above definition) based on these values. The variable events is assumed to be a vector containing the events in the sample space of a discrete random variable X , and the variable probabilities is assumed to be a vector containining the respective probability of each event. You can make use of the expected.value function from the W'eek 2 Lab class in your code. You may also nd it helpful to model your solution on the functions in this lab. (b) Use your function to verify that the generalised mean with exponent k = 2 of the random variable X in Question 1 is approximately 6.162. For your interest: the generalised mean with. exponent 2 is speeieatiy known as the root mean square of the random variable. For Question 2, submit the code you write for part {a}, and the commands used to evaluate part (b)