Midterm Exam solutions 2017 Random Variables and Probability Distributions

1.The expected value of a random variable is defined as a. The value of the random variable on the next trial b. The value of the random variable after infinite trials c. The average value of the random variable after the next trial d. The average value of the random variable after infinite trials 2.Assuming 365 days in the year, what is the probability that at least 2 people share a birthday in your class of 36 students? 1 1− a. 365 ! ( 365−36 ) ! 1 b. 1− 36 365 365 ! c. ( 365−36 ) ! 1−36536 365 36 1− d. 365 ! ( 365−36 ) ! 3.80% of the general public believes that top executives in investment banks are overpaid. In a sample of 10, what is the probability less than 5 believe the same? a. 0.0055 b. 0.0064 c. 0.0264 d. 0.0328 4. x N ( 20,5 )the mean is a. 0.16 b. 0.34 c. 0.68 d. 0.95 . The probability that a randomly selected x is greater than one standard deviation from 5.Which statement is false? a. The complement of an event is all events that don’t occur in the event. b. The complement of an event and the event are mutually exclusive c. The complement of an event and the event are independent d. The probability of the complement of A is 1-P(A) 6.Kobe Bryant of the LA Lakers made 381 out of 451 free throw attempts in the 2011-2012 NBA season. Based on this, we can use the _________________________ method to determine that the likelihood of his making his next free throw attempt is 0.845. a. Classical b. Subjective