44377

First replace any zero in your student ID with 5. For example, if your student ID is 36014, then it will change to 36514. Then, let N be the smallest digits of this number and M be the largest digits of this number. For instance, in the above example N=1;M=6; N= M= Important note: If you don't solve this assessment with the numbers taken from your student ID as explained above, all calculations and answers are considered to be wrong. Question 1: General discrete distribution (50 Points) Consider the probability mass function for the number of network disruptions (1) per week in a company x f(x)=P(X= x) F(x)=P(XS X) PMF CDF 0 M/20 1 0.1 2 0.1 3 N/20 4 0.05 5 a) Complete the above probability mass table (PMF) and the corresponding cumulative distribution table (CDF) (10 points) b) Find P(X = 5), (10 points) c) Find the probability of less than 3 network disruptions in a random week. (10 points) d) Calculate expected value of the number of network disruptions per week. (10 points) e) Calculate the variance and the standard deviation of number of the network disruptions per week. (10 points)