2. The table below presents the min January daily temperature in Montreal (Canada) in C. Day...
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2. The table below presents the min January daily temperature in Montreal (Canada) in °C. Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Min T (°C) Day -11 -15 -14 -3 -1 -12 -16 -10 -3 -13 -18 -18 -19 -19 -18 -8 17 18 19 20 21 22 23 24 Min T (°C) 29 30 31 -17 -20 -16 -25 -21 -21 -23 -13 25 -6 26 -10 27 -13 28 . ܝܐ -8 -5 -1 -1 a) Build a histogram of the data using bins such that 1:-25 ≤ T <-20 2: -20 ≤ T <-15 3:-15 ≤ T <-10 4: -10 ≤ T <-5 5: -5 ≤ T <0 What are N, AT, M and n,? M b) Verify that N = Σ n₁ = n₁ +n₁₂₁ + j=1 + n M c) Now let's convert the histogram constructed in a) into a probability density function for the same random variable. Calculate the probability density for each bin (p), where: P₁ = n/(NAT) d) Based on the probability density calculated in c), what is the probability that the January min daily temperature in Montreal lies between -25°C ≤ T < -20°C, i.e. Prob{-25°C ≤ T < -20}? And what are Prob{-20°C ≤ T < -15), Prob{-15°C ≤ T < -10), Prob{-10°C ≤ T < -5}, Prob{-5°C ≤ T < 0}? M f) Verify that Σ PAT = 1 /=1 e) Based on the probabilities calculated in d), which temperature range is the most likely? 2. The table below presents the min January daily temperature in Montreal (Canada) in °C. Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Min T (°C) Day -11 -15 -14 -3 -1 -12 -16 -10 -3 -13 -18 -18 -19 -19 -18 -8 17 18 19 20 21 22 23 24 Min T (°C) 29 30 31 -17 -20 -16 -25 -21 -21 -23 -13 25 -6 26 -10 27 -13 28 . ܝܐ -8 -5 -1 -1 a) Build a histogram of the data using bins such that 1:-25 ≤ T <-20 2: -20 ≤ T <-15 3:-15 ≤ T <-10 4: -10 ≤ T <-5 5: -5 ≤ T <0 What are N, AT, M and n,? M b) Verify that N = Σ n₁ = n₁ +n₁₂₁ + j=1 + n M c) Now let's convert the histogram constructed in a) into a probability density function for the same random variable. Calculate the probability density for each bin (p), where: P₁ = n/(NAT) d) Based on the probability density calculated in c), what is the probability that the January min daily temperature in Montreal lies between -25°C ≤ T < -20°C, i.e. Prob{-25°C ≤ T < -20}? And what are Prob{-20°C ≤ T < -15), Prob{-15°C ≤ T < -10), Prob{-10°C ≤ T < -5}, Prob{-5°C ≤ T < 0}? M f) Verify that Σ PAT = 1 /=1 e) Based on the probabilities calculated in d), which temperature range is the most likely?
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Related Book For
Operations management processes and supply chain
ISBN: 978-0136065760
9th edition
Authors: Lee J Krajewski, Larry P Ritzman, Manoj K Malhotra
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