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Assignment Task :

Question 1 (this question has three parts, (a), (b) and (c)) 

(a) Consider the following probability distribution function for the 

discrete random variable X. Calculate E(3X2 + 5). 

X 2 3 4 f(X) 0.45 0.34 0.21 

 

(b) The following joint probability distribution function table shows the likelihood of the number of times (X) different age groups of people (Y) have left their house each week for any reason during the COVID-19 crisis. Note that X = 1, 2 and 3. The variable Y = 1 (Young), 2 (Middle aged), 3 (Old) and 4 (Very old). Calculate Cov (X,Y). 

(c) During the COVID-19 pandemic, it has been observed that for a selected group of countries, the number of new cases recorded has a normal distribution with a mean of 102, and a standard deviation of 127. Find: 

(i) P(50 < X < 150) (ii) What is the probability that on any one day in one of these countries, less than 10 new cases will be recorded?

 

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