Question

At least one of the answers above is NOT correct. 3 of the questions remain unanswered 6 points) The following density function describes a random variable X f(z) = f(z) = 181z if 9 < z < 18 if 0<z<9 and Draw a graph of the density function and then use it to find the probabilities below A Find the probability that X lies between 2 and 7 Probability 302469 B. Find the probability that X lies between 6 and 11. Probability C. Find the probability that X is less than 10 Probability D. Find the probability that X is greater than 5 Probability Note: You can earn partial credit on this problem. Preview My Answers Submit Answers Your score was recorded

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Answer 1

f(x) = {x/81 18-x/81 0 < x < 9 9 < x < 18 (A) P(2 lessthanorequalto times lessthanorequalto 7) = integral^7_2 x/81 dx = 1/81 (x^2/2)^7_2 = 1/162 (7^2 - 2^2) = 1/162 (49 - 4) = 45/165 = 0.27778 (B) P(6 lessthanorequalto x lessthanorequalto 11) = integral^9_6 x/81 dx + integral^11_9 18 - x/81 dx = 1/81 (x^2/2)^9_6 + 1/81 (18x - x^2/2)^11_9 = 1/81 [1/2 (9^2 - 6^2) + (198 - 121/2 - 162 + 81/2)] = 1/81 (45/2 + 36 - 20) = 77/162 = 0.475386 (C) P(x < 10) = integral^9_0 x/81 dx + integral^10_9 (18 - x/81) dx = 1/81 (x^2/2)^9_0 + 1/81 (18 x - x^2/2)^10_9 = 1/81 [1/2 times 81 + (180 - 50 - 162 + 81/2)] = 1/81 [81/2 - 32 + 81/2] = 46/81 = 0.6049383 (d) P(x > 5) = 1 - P(x lessthanorequalto 5) = 1 - integral^5_0 x/81 dx