REDMI NOTE 8 48MP QUAD CAMERA Assignment # 2 1. (3 marks) If you rolled 6 dice at the same time, and your experiment is to determine the smallest number among the six dice. a. (2 marks) Find the expectation of your experiment. b. (1 marks) Calculate the standard deviation. 2. (3 marks) You have X male students and Y female students in a class. You choose a registration number from a list (without knowing the gender of the student) at random and without replacement. When ALL male students have been selected, your experiment is finished. What is the expected number of female students not selected by the end of the experiment? 3. (3 marks) A machine contains to major parts: electrical and mechanical. As the two parts are working properly, there is no problem in the machine, but if any of them fails, the machine will stop producing items. Given the JPDF of the machine parts (X: Electrical, Y: Mechanical) in hours. (x + y fxx(x, y) = 0 < x <2, 0 < y < 2 8 0 else What is the probability will stop producing items within one hour? 1. (3 marks) Family "A" calculated their monthly expenses, and found to be a random variable with distribution fx (x). Another family "B" finds that their expenses are twice what family "A" used to spend each month. Find fy(y) which is the distribution of family "B" in terms of fx (x). Note: fy(y) 0 END OF ASSIGNMENT-