Question

Question 2 (10 points) A lazy taxi driver makes exactly three trips each day. For each of the past 200 days shes been working, she has recorded the number of rides that earned her more than $25. She calls these good rides. It is reasonable to assume that her trip earnings form a random sample. She collects the following data: Number of good rides Number of days 80 26 For instance, she had 23 days without any good ride. In your final expression, write down the formula and plug in the values of each variable you use. Do NOT leave variables (for example , n) without plugging in their values. Do NOT simplify the fractions or partially calculate your formula. 1. Write yi = 1 if the i-th ride is a good one, and yi = 0 otherwise; then y1, ..., 4600 is a random sample. Calculate its sample mean and sample variance. 2. Suppose that stands for the number of days with k good rides. A friend proposes to use the estimator for the population proportion of good rides. What is the bias of ô?

Answer 1

If Yi=1 ; ith ride is good one then y... Yoo is a random sample is given 0.97622, 0.07262, Ra So. 05716, 0.1964 ---- T 0.28212 9600 A = 600 obs? Mean of random sample = Exi η 284.4095 Goo x-0 -0.4760 vanance - Exiz = 0. 08803 08803 2 ô - I ( 1 Ni+ ? N2 + N) 200 Ni = 80 N2 = 71, N3= 26 biascã )= EC ) - 0. = E zoo Gf Nit}N 2+ N3 ) ) - 0.4740 = o(+*80 + { x71+26) – 014740 - I 0.5-0.4740 bịas Cô)= 0.02598