Topic2_RandomVariables_TestReview.pdf - ECO220Y5Y Quantitative Methods in Economics Topic Two \u2013 Random Variables Probability Test Review Questions

Topic2_RandomVariables_TestReview.pdf - ECO220Y5Y...

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ECO220Y5Y: Quantitative Methods in Economics Topic Two – Random Variables & Probability Test Review Questions Tutorials – Fall/Winter 2017/18 Consider the random phenomenon of selecting a playing card from a deck of 52: 1. What is the probability of selecting the King of Hearts? 2. What is the probability of selecting the King of Hearts or the King of Clubs? 3. What is the probability of selecting a King or Queen? 4. Assume you draw a card observe it, replace it in the deck and then draw a second card; given the first draw was a King of Hearts what is the probability of the second draw being a King? Tutorials – Fall/Winter 2017/18 Consider the data above on monthly average gas prices in Mississauga: 1. What is the probability that an individual selected at random believes that global warming is a series issue? What type of probability is this? 2. What is the probability that an individual selected at random is a Conservative and believes that global warming is a series issue? What type of probability is this? 3. What is the probability that an individual selected at random believes that global warming is a non issue given that the individual is a Liberal? What type of probability is this? 4. What is the probability that an individual selected at random is a Liberal given the individual believes that global warming is a series issue? What type of probability is this? 5. Are political party affiliation and opinion on global warming independent? Explain your answer. page 1 of 10
ECO220Y October 16, 2019 Tutorials – Fall/Winter 2017/18 One argument for the lack of high wage jobs for new immigrants vs. Canadian born is due to unequal social networks (strong vs. limited social networks). A recent random survey of high wage earners found that 80% were Canadian born. Moreover, 75% of those who were surveyed had strong social networks but only 15% with a strong social network were new immigrants. 1. Construct the contingency table. 2. Are the two events, N = (a randomly selected high wage earner is a new immigrant) and L = (a randomly selected high wage earner has limited social networks) independent? Explain. Tutorials – Fall/Winter 2018/19 .2 .2 .3 .3 .5 .5 0 0 .1 .1 .2 .2 .3 .3 .4 .4 .5 .5 Density Density 0 1 1 2 2 X X .6 .6 .3 .3 .1 .1 0 0 .2 .2 .4 .4 .6 .6 Density Density 2 2 3 3 4 4 Y Y 1. Use the marginal distributions to complete the following contingency table showing joint probabilities for the bivariate distribution of X and Y (solve for a, b, c) 2. What is the probability X = 0 given Y = 2? What is the probability Y = 2 given X = 0? 3. Write out the distribution of X 2 Y 2 and solve for E[ X 2 Y 2 ] Tutorials – Fall/Winter 2018/19 Assume X and Y are random variables where we know E(X) = 6, V(X) = 4, E(Y) = 10, V(Y) = 5, COV(XY) = - 2 1. Solve for E[2 + 5 X - 6 Y ] 2. Solve for SD[2 + 5 X - 6 Y ] page 2 of 10
ECO220Y October 16, 2019 Now assume we introduce the random variable Z where we know: V(Z) = 3, COV(YZ) = 3, SD[2 + 5 X - 6 Y + 10 Z ] = 20.

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• Spring '14
• Schmid
• Probability, Probability theory, Probability space, Joint probability distribution, Marginal distribution

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