Revision of Statistics ecotrix

Revision of Statistics ecotrix - Transcript

ECON 14 Introductory Econometrics
PROBLEM SET 2A
Topic 2 Revision of Statistics
A and B are two events Can they be mutually exclusive and independent simultaneously
If we twice flip a balanced coin what is the probability of getting at least one head
A die is loaded in such a way that each odd number is twice as likely to occur as each even number Find P G where G is the event that a number greater than 3 occurs on a single roll of dice
Four economists have predicted the following rates of growth of GDP for the next year E1 below 2 percent E2 2 or greater than 2 but below 4 E3 4 or greater than 4 but less than 6 E4 6 or more Let Ai be the actual rate of GDP growth rate according to the same four classifications as Ei a Are the events E1 through E4 mutually exclusive Are they collectively exhaustive b What is the meaning of the events E1A2 E2 A3 Ei Ai EiAj where I J
A die is loaded in such a way that each odd number is twice as likely to occur as each even number What is the probability that the number of points rolled is a perfect square What is the probability that it is a perfect square given that it is greater than 3
If A B and C are any three events in a sample space S such that P A intersection B not equal to zero Then P A B C P A P B A P C A C
The completion of a construction job may be delayed because of a strike The probabilities are 0 60 that there will be a strike 0 85 that the construction job will be completed on time if there is no strike and 0 35 that the construction job will be completed on time of there is a strike What is the probability that the construction job will be completed on time
If A B and C are any three events in a sample space S then P A B C P A P B P C P A B P A C P B C P A B C
The PDF of a continuous random variable X is as follows
f X c 4x 2x2 o x 2
o otherwise
For this to be a proper density function what must must be the value of c
Find P 1 x 2
Find P x 2
Check whether the function given by f x x 2 25 for x 1 2 3 4 5 can serve as the probability mass function of a discrete random variable
Find the distribution function of the total number of heads obtained in four tosses of a balanced coin
If X has the probability density as f x k e 3x for x 0 0 otherwise
Find the distribution function of the random variable X and use it to evaluate P 0 5 X 1
Find the probability function for the random variable X whose distribution function is given as
F x 0 for x 0
x for 0 x 1
1 for x 1
Also plot the graph
Determine the value of k for which the function given by f xy kxy for x 1 2 3 and y 1 2 3 can serve as a joint probability distribution
Given the joint probability density function f x y 3 5 x y x for 0 x 1 and 0 y 2 of two random variables X and Y Find P X Y A where A is the region x y 0 x 1 2 1 y 2
If the joint probability distribution of X and Y is given as f x y 1 30 x y for x 0 1 2 3 and y 0 1 2 Construct a table showing the values of the joint distribution function of the two random variables at the twelve points 0 0 0 1 3 2
Two tablets are selected at random from a bottle containing three aspirin two sedative and four laxative tablets If X and Y are respectively the numbers of aspirin and sedative tablets included among the two tablets drawn from the bottle find the probabilities associated with all possible pairs of values of X and Y Find the probability distribution of X alone and Y alone
Given the joint probability density
f x y 2 3 x 2y for 0 x 1 0 y 1 and 0 otherwise
Find the marginal densities of X and Y
With reference to problem 17 find the conditional probability of X given Y 1
With reference to problem 18 find the conditional probability of X given Y y and use it to evaluate P X 1 2 Y 1 2
With reference to problem 17 find the expected value of g X Y X Y
If the joint probability density function of X and Y is given as
f x y 2 7 x 2y for 0 x 1 and 1 y 2 and 0 otherwise
find the expected value of g X Y X Y3
1 x2 for 0 x 1 and 0 elsewhere
With reference to problem 17 find the conditional mean of X given Y 1
If the Joint probability density of X and Y is given as
f x y 2 3 x 2y for 0 x 1 and 0 y 1 and 0 elsewhere






2
variance of X given Y 1 2
Readings
Gujarati D N 2006 Essentials of Econometrics McGraw Hill Asia Chap 2 3