Question

Q4. [25] The gardening company wants to statistically analyze his yearly harvest of peas. For every pea pod he picks he measures its length x; in centimeters and its weight yi in grams. He divides the peas into two classes, the good and the bad (empty pods). The measured data (Xi, yi) are Good peas: x 2 y 2 2 3 2 4 3 4 3 4 4 5 4 6 5 5 5 6 6 6 Bad peas: y 1 2 2 3 3 1) [5] Compute the probability of the peas that are 23 grams in good peas. 2) [5] Compute the probability of the peas that are 23 grams. 3) [5] Compute the probability of the good peas. 4) [5] Compute the probability of the good peas in the peas which are 2 3 grams. 5) [5] Compute the probability of the good peas in the peas which are < 3 grams. Instruction: For each question, do NOT verbally describe what & how to compute it but define what needs to be compute and show the computational steps precisely. 1. Define the variables e.g.) A: Alarm, F: Fire, or use the defined variables: e.g.) Ez and B, etc. in Q2, TA, TB, V, etc. in Q3, etc. 2. Define what needs to be computed: e.g.) P(A|F) 3. Derive the formulas for computation, step by step: e.g.) P(A|F) = P(F| A):P(A) 4. Assign the values to the derived formula to complete the computation. e.g.) P(A|F) = P(F|A).P(A) = 0.2.0.6 = 0.12

Answer 1

Answer let xi be length in centimeters and yi be weights in grams for ith pea. The measured data (xi, y;) is Good peas x 2 2 2 3 3 4 4 5 5 6 Y 2 3 4 4 4 5 6 5 6 6 Bad peas x 3 4 6 6 7 y 1 2 2 3 3 1 There are 10 Good peas and 5 bad peas so that total number of peas are 15. The classical definition of prob is PLA= No. of favourable events for A Total number of events where PLA) is probability of event A The number of the peas whose weights are greater than or equal to 3 grams in good peas = g. Total no. of good peas - 10 Hence the required probability = I= 0.9 (bring (is) The total number of peas = 15 The number of peas whose weigthe 73 grams = 9 tol in good pras) + 2 (in bad pecu) = 11 Hence the prob that peces are 23 grams is given by using cil, whic in = 1 0.73. 2) 13

a The total humber of peau = 15 The numer of good peces = 10 Hence the probability of good peas the number of good peas = the total no. of peas 10 20.67 15 4) 5) The total number of peas whose weights are greater than or equal to 3 grams = 11. The number of good peas whose weights are greater than or equal to 3 grams = 9. Hence the probability of good reas in the Reas which are 23 quums = 9 0.818.1 ♡ 0.82. The total number of peas whose weights are less than 3 grams = 4 The number of peas (good) whose weights are less than 3 grams = 1 Hence using the classical definition of probability given incil, the required probability is P( good peas in the peas which are 3 grams) 10.25