Question 1

{a} Consider the following probability distribution function for the discrete random variable X. Calculate EIKE + 1]. "m- {3 marks] {b} The following joint probability distribution table represents the likelihood COMB19 infection, by the frequency of applying hand sanitisers per day {X}, and age groups {Y}. The variable Y is defined as: Y: 1 {Young}, 2 [Middle aged}, and 3 {Old}. Calculate Cole,'r'}. 1 1110 0.03 [vauns] 2 Y . 13.13 13.12 0.35 {m-ddleaae} --- 3 [old] {4 marks] {c} In July, the daily maximum temperature in Melbourne follows a normal distribution with a mean of 14C, and a standard deviation of 3C. [i] Find the probability that the maximum temperature on a given day is below 8C. {ii} In January the daily maximum temperature in Melbourne follows a normal distribution with a mean of 26C and a standard deviation of 5C. Compare the two events of having a 4DC day in January with having a 213C day in July, which event has a higher probability of occurring? 2