Bridges Math 115bTIPS FOR TEST 2 AND FOR THE FINAL EXAM1. Know and understand what the formulas on your List of Formulas sheet mean.2. Memorize the formula for the Confidence Interval – it is not on the List of Formulas.(´x−z0∙ s√n, ´x+z0∙ s√n). On Test 2, if the 95% confidence interval is asked for, then I will tell you that z0=1.96.On the Final Exam, the value of z0 will be given to you like this: “Use the fact that P(−1.96 ≤ Z ≤1.96)=0.95 to find the 95% confidence interval.”3. Make the graphs that you draw clear. Always label the axes and give your graph a title. Also writethe units on the axes. If you are to graph something, for instance, from the years 1995 to 2001 andyou want the data at 1995 to be at the origin, then state: “The year 1995 corresponds to x=0.”4. Know and understand what the formulas on your List of Formulas sheet mean.5. If you are in doubt as to whether or not work should be shown, then show it.6. Do not round your calculations in the middle of a problem. Keep all decimal places until the end of the problem.7. Write all answers rounded to 4 decimal places, unless you are instructed otherwise. If the answer divides evenly (for example, 20.82 / 13.0125 = 1.6), then you can write your answer as 1.6 or you can write it as 1.6000. 8. Suppose during Test 2 or during the Final Exam you ask me, “To how many decimal places do you want this answer?” Then I will take off 1 point from your score for not paying attention.9. Know and understand what the formulas on your List of Formulas sheet mean. Yes, I know I’ve written this 3 times. Here is an example:FIND THE VALUE OF EACH OF THESE INTEGRALS:(a)∫−∞∞x(17√2 π∙ e−0.5(x−257)2)dx(b)∫−∞∞(17√2 π)e−0.5(x−257)2dx(c)∫−∞∞(x−25)2∙(17√2 π∙ e−0.5(x−257)2)dxIF YOU CAN’T GIVE THE VALUE OF EACH OF THESE INTEGRALS QUICKLY, THEN YOU DON’TUNDERSTAND THE FORMULAS ON THE List of Formulas SHEET. ANSWERS ARE 1Bridges Math 115bON PAGE 2.10. Here’s another problem straight from the Final Exam Study Guide:The pdf of a random variable X is given below. Set up, but do not evaluate, an integral that gives E(X).fX(x)={0 if x ←1x23if −1 ≤ x ≤ 20 if x >2}You are always expected to give the very best answer possible. So on a problem like this, if someone answered E(X)=∫−∞∞x ∙ fX(x)dx , then that person would receive no credit at all. The question asks for E( X) and all this person has done is to copy the formula from theList of Formulas.The best answer to this problem is: ∫−12x ∙x23dx. ANSWERS TO PROBLEM #9:(a) 25 The integral is the formula for the expected value of the pdf of a normal random variable. Within this formula we can see that the mean of this normal random variable is 25 and that the standard deviation is 7.(b) 1 The integral is the formula for the pdf of a normal random variable. The area under any pdf is 1.(c) 49 The integral is the formula for the variance of the pdf of a normal random variable. Within this formula we can see that the mean of this normal random variable is 25 and that the standard deviation is 7. We want the variance, so we square the standard deviation of
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