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Engineering Probability And Statistics Exercises

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Engineering Probability And Statistics 1. a. Define what we mean by the sample space of an experiment Sample Space is the set of all possible outcomes of an experiment b. Suppose an experiment consists of throwing together a coin and a dice. So one outcome could be Heads, 3 and we write it as H3. List all elements of the sample space of this experiment and what is the size of the sample space? 𝑆 = {𝐻1, 𝐻2, 𝐻3, 𝐻4, 𝐻5, 𝐻6, 𝑇1, 𝑇2, 𝑇3, 𝑇4, 𝑇5, 𝑇6} 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒 = (21 )(61 ) = 12 c. Let A be the event of getting an odd number on the dice. List all elements in A. 𝐴 = {𝐻1, 𝐻3, 𝐻5, 𝑇1, 𝑇3, 𝑇5} d. What is the probability of the event A? 𝑛𝐴 6 𝑃(𝐴) = = = 0.5 𝑛𝑆 12 e. Let B be the event of getting a number higher than 5 on the dice. List elements of B. 𝐵 = {𝐻6, 𝑇6} f. Compute the probability of B 𝑛𝑏 2 1 𝑃(𝐵) = = = ≅ 0.1667 𝑛𝑠 12 6 Engineering Probability And Statistics 2. Among 6 applicants for an open position, 4 are females and 2 are males. Suppose three applicants are randomly selected from the applicant pool for final interview. Find, a. The probability distribution of X, the number of female applicants among the chosen three. 𝑛 = 𝑁𝑢𝑚. 𝑜𝑓 𝑊𝑜𝑚𝑒𝑛 𝑡𝑜 𝑠𝑒𝑙𝑒𝑐𝑡 𝑓𝑟𝑜𝑚 (𝑛𝑥)(𝑁−𝑛 ) 𝑥 = 𝑁𝑢𝑚. 𝑜𝑓 𝑊𝑜𝑚𝑒𝑛 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑍−𝑥 ...
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