MEM 361 Engineering Reliability
Problem Set 1
1) Let the random variable X be defined as the product of the two numbers when 2 dice
are rolled.
• List all possible values of X by this mechanism;
• Determine the theoretical probability function, f(x);
• Sketch a bar-chart for f(x);
• Compute F(25), explain the meaning of F(25);
• Compute R(15), explain the meaning of R(15);
• Show that the sum of all possible value of f(x) equals to one.
2) A coin-bag contains 3 pennies, 2 nickels and 3 dimes. If 3 coins are to be taken from
the bag each time, their sum is then a random variable: X.
• List all the possible values of X by this mechanism;
• Determine the associated probability distribution f(x);
• Plot the distribution as a bar-chart;
• Show that the sum of all possible value of f(x) equals to one.
3) Let the random variable X be the sum of the three numbers when 3 dice are rolled.
• Complete the theoretical probability distribution f(x) for X;
• Show your results in a bar-chart;
• Comment on the form of the bar-charts obtained by rolling 1, 2 and 3 dice,
respectively.
4) The Boeing 777 is designed for a mean service life of 20 years in normal use. Let the
service life distribution be given by f(t), where t is in years. If a B-777 has been in serve
for 10 years already, what is the chance that the craft is still fit to fly until for another 6
years?