STAT 401 Section 1 Questions from first Mid term Spring 2004 Question 1 Suppose that Y is a normal random variable with mean 12 and variance 25 Which of the following is closest to P 7 Y 17 A 95 B 50 0 C 99 7 D 68 Question 2 Suppose the joint pmf of X and Y is given by y 1 2 x 1 k 3k 2 3k k What is k A 1 B C D 1 4 1 8 1 3 E None of the above Question 3 Which one of the following random variables is discrete A B is a binomial 5 2 random variable B Z is a standard normal random variable C E is an exponential random variable with parameter 2 D X is a random variable with density function f x k 1 x2 for some value of k E None of the above Question 4 Suppose that we perform an experiment consisting of flipping a dime a nickel a penny and a quarter Let S denote the sample space for this experiment In other words S consists of the 16 outcomes HHHH HHHT T T T T Suppose that A is the event that the quarter comes up heads How many outcomes are contained in A A 2 B 8 C 4 D 16 E None of the above Question 5 A personnel director will interview 14 job candidates in random order of whom 9 have master s degrees If she interviews 7 of the candidates on the first day what is the probability that she will interview 2 people with master s degrees on the first day A 2 9 B 55 0159 14 7 9 2 5 5 0504 2 14 14 9 5 2 5 14 7 C 0105 9 5 14 9 D 2 7 5 7 0047 E None of the above Question 6 A probability experiment consists of simultaneously rolling a six sided die flipping a coin and selecting one card at random from a standard 52 card deck How many outcomes are contained in the sample space for this experiment 52 52 6 2 A 20 359 846 B 6 2 52 60 C 6 2 52 624 D 6 2 52 3 216 000 E None of the above Question 7 Suppose that X is a random variable with probability density function given by f x kx2 0 0 x 1 otherwise Let E X What is the value of k A 3 25 B 3 5 C 4 D 3 75 E None of the above Question 8 Suppose that P A and P B both equal 31 Furthermore suppose that A and B are independent events What is P A B A B C D 7 9 6 9 5 9 3 9 E None of the above Question 9 Suppose that 25 of the people who make purchases in a particular electronics store buy an expensive item costing more than 100 Of those who buy these expensive items 80 use credit cards to make their purchases Of the customers who do not buy an item costing more than 100 only 40 use credit cards Suppose we are told that a shopper used a credit card to make a purchase What is the probability that that shopper bought an item costing more than 100 2 667 3 1 B 25 4 1 C 20 5 2 D 40 5 E None of the above A Question 10 Assume that you are given the following information about events A1 A2 and A3 P A1 A2 25 P A1 A3 20 P A2 A3 35 P A1 A2 A3 15 What is the probability of the shaded event depicted in the Venn diagram accompanying this question A 60 B 80 C 50 D 70 E None of the above Question 11 Suppose X1 and X2 are independent random variables with E X1 3 and E X2 1 What is E 3X1 4X2 10 A 9 B 1 C 15 D 5 E None of the above Question 12 Suppose that X1 X20 are independent random variables each with mean 120 1 P20 and variance 100 Let X denote the sample mean 20 i 1 Xi What is V X A 10 B 6 C 5 D 120 E None of the above Question 13 For events A and B suppose P A 4 and P B 5 and P A B 8 Which of the following is equal to P A B A 4 B 3 C 2 D 5 E None of the above Question 14 Suppose that 25 of all drivers are older than 50 10 of all drivers have gotten a speeding ticket in their lives and 5 of all drivers are older than 50 and have gotten a speeding ticket in their lives What percent of drivers older than 50 have ever gotten a speeding ticket A 40 B 10 C 30 D 20 E None of the above Question 15 Suppose that the random variable Y can only take the values 1 2 and 3 Its probability mass function satisfies P Y y ky for y 1 2 3 What is the value of k A 1 B k cannot be determined without knowing the expectation of Y C D 1 2 1 3 E None of the above Question 16 Suppose that X is a continuous random variable with cdf F x 0 x 3 2 1 x 3 3 x 5 x 5 What is the median also known as the 50th percentile of X A 3 5 B 3 75 C 4 D 4 25 E None of the above Question 17 Suppose I have a fair 10 sided coin i e a coin with 10 faces for which each face comes 1 up with probability 10 I roll this coin 400 times Let N denote the number of times the number 9 comes up Which of the following is the best approximation for P 39 N 50 A 9 5 6 0 5 6 477 B 400 400 139 9361 150 9350 050 39 50 C 400 140 9360 066 40 10 5 D 6 1 5 6 559 Question 18 Suppose that X and Y are jointly distributed with joint density f x y kxy 0 0 x 1 0 y 1 otherwise What is k A 2 B 3 C 1 D 4 E None of the above Question 19 Suppose that X has cumulative distribution function cdf given by 0 2 3 x 0 0 x 1 1 x 2 F x 5 2 x 3 6 3 x 4 8 4 x 5 1 5 x What is P 2 X 4 A 3 B 4 C 6 D 5 E None of the above Question 20 Suppose that B is a binomial 10 3 random variable If Y 7B 22 what is the expected value of Y A 3 B 2 1 C 0 D 1 E None of the above Question 21 Suppose that a fast food restaurant runs a promotion in which 10 of all its soft …