Eco 400

1. {Expected value calculation, discrete random event} Suppose you have a coin that lands on Heads with probability 0.6. Where the random variable X is the sum of two coin flips, (where heads count 1 and tails count o - two heads then X= 2, a head and a tail then X = 1 and two tails the X = o). Compute the expected value of X.2. {Expected value calculation, discrete random event} Suppose you have a fair coin. Where the random variable X is the sum of three coin flips, (where heads count 1 and tails count o - three heads then X= 3, two heads and a tail is X = 2, just one head has X=1, and with three tails X = o). Compute the expected value of X.3. {Probability} How many times do you need to flip a fair coin so that the probability of getting ALL heads is less than 0.0014. {Expected value of mean and variance estimators, systematic error and mean zero error} You have a sample from a survey where people report how much they smoke. The problem is people under-report how much they smoke because they are embarrassed and they also don't remember exactly how much they smoke. If x; is the number of cigarettes person i reports smoking, then x = x/ + up (where x/ is the true number of cigarettes person i smoked, and u; is their reporting error.) The misreporting is independent of the true number of cigarettes consumed and E[u ] = /y and the Var(u) = of and is uncorrelated with the number of cigarettes actually smoked (cov(x*, u) = 0) a. What is the expected value of the sample mean in terms of the population mean of cigarettes smoked? E[/}] =??b. Is the sample mean an unbiased estimate of the number of cigarettes smoked? If not, how far off is it?c. What is (i.e. derive) the expected value of the variance of the variable x, E Var(x) = E[ox] =??d. What is (i.e. derive) the expected value of the variance of the sample mean E[Var(A,)] =?b. Now let's add one more country to the data Chad, Literacy Rate = 37.6 Repeat the exercise in A.5. {hand calc mean, variance and standard deviation, simple summary stats with R} The following table shows literacy rates among the youths (age 15- 24) for some of the countries in Sub Saharan Africa Country Literacy Rate (%) Angola 72.2 Burundi 73-3 Democratic Republic of Congo 70.4 Rwanda 77.6 Kenya 80.3 a. Calculate mean and median. Also calculate variance and standard deviation