STAT 500 Homework 4 Answers (Penn State University) Latest Verified Review 2023 Practice Questions and Answers for Exam Preparation, 100% Correct with Explanations, Highly Recommended, Download to Score A+

STAT 500 Homework 4 Answers (Penn State University) Latest Verified Review 2023 Practice Questions and Answers for Exam Preparation, 100% Correct with Explanations, Highly Recommended, Download to Score A+ 1. Are you someone who prefers to take risk or avoid risk? I tend to avoid risks. A. You are given $5,000 to invest. You must choose between (i) a sure gain of $2,500 and (ii) a 0.50 chance of a gain of $5,000 and a 0.50 chance to gain nothing. What is the expected gain with each strategy? Which strategy do you prefer (this is an opinion so no right answer!)? For (i) the gain is $2500 with certainty. For (ii) the expected gain is 0.5*0 + 0.5*5000 = 2500. So the gain is the same, but I prefer option (i) since there is no risk. B. You are given $10,000 to invest. You must choose between (i) a sure loss of $2,500 and (ii) a 0.50 chance of losing $5,000 and a 0.50 chance to lose nothing. What is the expected loss with each strategy? Which strategy do you prefer (this is an opinion so no right answer!)? The expected loss for (i) is $2500 with certainty, and for (ii) it is 0.5*0+0.5*5000 = $2500. So again, the loss is the same for both options. I prefer (ii) here since I could potentially lose less. 2. A professor always assigns final grades such that 20% are A, 40% are B, 30% are C, 5% are D, and 5% are F. The grade point scores are 4 for A; 3 for B; 2 for C; 1 for D; and 0 for F. A. Create the probability distribution table for grade points for this professor. X = grade 0 1 2 3 4 P(X=x) 0.05 0.05 0.3 0.4 0.20 B. Find the mean of this probability distribution and provide and interpretation of this mean. E(X) = 0.05*0 + 0.05*1 + 0.3*2 + 0.4*3 + 0.2*4 = 0.05 + 0.6 + 1.2 + 0.8 = 2.65 C. Find the variance and standard deviation. V(X) = [0.5*0^2 + 0.05*1^1 + 0.3*2^2 + 0.4*3^2 + 0.2*4^2] – 2.65^2 = 1.03 SD(X) = sqrt( V(X) ) = sqrt (1.03) = 1.01489