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Unformatted text preview: Sample Quiz 1 to be solved in class This is a closed book, closed notes quiz. You may use one 8 1/2 by 11 inch help sheet. 20 points
1) A guidance counselor is planning schedules for 30 students. Sixteen students say they
want to take French, 16 want to take Spanish, and 11 want to take Latin. Five say they want to take both French and Latin, and of these, 3 wanted to take Spanish as well. Five
want only Latin, and 8 want only Spanish, 3) How many students want French only? b) What is the probability that a randomly selected student would Want to take French
and Spanish? 10 points
2) When Kimberly was shopping for her car, she found that there were 72 possible combinations of engines, body types, and colors. Her choices included four choices of
engines and three choices of body types. how many choices of colors does she have? 30 points 3) Suppose it is known that 1% of the population suffers from a particular disease. A
blood test has a 97% chance of identifying the diseased individuals, but also has a 6%
chance of falsely indicating that a healthy person has the disease. a) What is the probability that a person will have a positive blood test? b) If your blood test is positive, what is the chance that you have the disease? 0) If your blood test is negative, what is the chance that you "do not have the disease? 20 points
4) Suppose the probability density function for the continuous random variable X is given
by
f(x)=kx5’3 0<x<l
= 0 otherwise a) Find k such that f (X) satisfies the properties of a probability density function
b) Find the median value 20 points
5) A device runs until both of two particular components fail, at which point the device stops running. The joint probability density function of the time to failure of these two
components measured in hours is _x+y
f(x!y)_ Calculate the prob ability that the device fails during its first hour of operation. forOSxS3andOSyS3 Sample Quiz 1 to be solved as practice by students
This is a closed book, closed notes quiz. You may use one 8 1/2 by 11 inch help sheet. 1. (15 points) Ten people in a room are each wearing a unique badge marked 1 through
10. Three people are chosen at random and asked to leave the room simultaneously. Their
badge numbers are noted. a) What is the number of ways these three people can be chosen .if order does not matter?
b) What is the probability that the smallest badge number of the three who leave is 5? 2. (20 points) A commuter who works in New York must either go through the Lincoln
Tunnel or across the George Washington Bridge to get home. He varies his route,
choosing the tunnel with probability 1/3, the bridge with probability 2l3. If he goes by
tunnel he gets home by 6 0’ clock 75% of time; if he goes by bridge, he gets home by 6
o’ clock only 60% of the time, but he likes the scenery better that way. a) What is the probability of his reaching home by 6 o’ clock?
b) If he gets home after 6 o’ clock, what is the probability that he used the bridge? 3. (15 points) The loss due to a fire in a commercial building is modeled by a random variable X with dollar loss expressed in units of $100,000. The probability density
function is, f(x) = k (20—X) for 0<X<20
= 0 otherwise. a) Find the appropriate value of k.
b) Find the mean loss in dollars due to fire. 4. (25 points) The probability mass function for the random variable, X, is given below: a) Find mean value for X.
b) Find the variance.
e) Find the expected value of X2 + 2X + 3 5.(25 points) Two electronic components, A and B, of a phone switching system work in
harmony for the success of the total system. Let X denote the time to failure in years of
component A and Y the time to failure of component B. The joint density function of X and Y is
given by,
f(x,y)=4x(2—y) for0<x< l, l <y<2 = 0 otherwise
a) Determine the marginal probability density function for X.
b) Determine the Probability of Y< 1.5 given that X = 0.5. ...
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 Spring '09
 chavez

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