Students_Tutorial answers Tutorial_5

So 1 2 11375 1067 000 005 010 015 020 025 030 035 040

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𝑋 ) So 𝑠 . 𝑑 . ( 𝑌 ) = [ 𝑣𝑎𝑟 ( 𝑌 )] 1 2 = 1.1375 = 1.067 . 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 1 2 3 4 5 Probability Number of increases Stock index increases over 5 years
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4. In each of the following cases X is a count. Does it have a binomial distribution? Justify you answer in each case. (a) You observe the sex of the next 20 babies born at a local hospital; X is the number of girls among them. Yes Recall our concerns about the gender composition example used in lectures: the fertility decision about whether to have a third child or not being impacted by the gender mix of the first two children; possibility of multiple births. These are not relevant here. Independence across trials now refers to births to different women and having a girl is not contagious! (b) A couple decides to continue to have children until their first girl is born; X is the total number of children the couple has. No Here n is not fixed and depends on previous trial outcomes. 5. The amount of petrol sold daily by a service station is known to be uniformly distributed between 4,000 and 6,000 litres. What is the probability of sales on any one day being between 5,500 and 6,000 litres? 𝑓 ( 𝑥 ) = 1 2000 𝑖𝑓 4000 ≤ 𝑥 ≤ 6000 = 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 ∴ 𝑃 (5500 ≤ 𝑋 ≤ 6000) = 500/2000 = 0.25
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