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r STAT 35000-336 21325: Homework 4 PROBLEM 2 Homework problems from the textbook: 5.8, 5.12, 5.32, 5.36, 5.67, 6.6, 6.8, 6.14, 6.45 Extra problems: Problem 1 A satellite system consists of 4 components and can function adequately if at least 2 of the 4 components
are in working condition. If each component is, independently, in working condition with probability 0.6,
What is the probability that the system functions adequately? Let X: #Quucﬂ-Congwﬁ CWKJQNLN‘ZS Mogq
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~:= [~— binomcdlt g4” B, D = ' 3209 Suppose that a particular personal trait 4 like eye colour or handedness — 1s lass1fied on the basis of one pair of genes. Let d denote a dominant gene and r a recessive. one. A person with do! genes is “purely dorninan ", one with 7'? genes “purely recessive", and one with 1rd genes a “hybrid”. Purely dominant and hybrid individuals are alike in appearance with respect to the trait in question. Children receive one gene from each parent. If, with respect to a particular trait, two hybrid parents have a total of four children, What is the probability that exactly three of the four children have the outward appearance of the dominant gene? Assume that each child is equally likely to inherit either of two genes from each parent. Phanei‘ﬁpe: x=i 5% AijAT)TA \ 3422, ”5 W“
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:iox‘noMpdfCAr, £1,130 : .1494 ($75 Page20f5 .QZog 7.1:] 1 ‘_‘_'. .2 ' " " “4 4'4” "-3 '2'“ .. _ _ -_ . ._ STAT 35000-SBC 21325: Homework 4. PROBLEM 3 Problem 3- We will ensuine that. the smiling times, in seconds, for an eight—week old baby, follow a. uniform distribution
between D and 23 seconds, inclusive. 1. What is the probability that a randomly chosen eight—week old baby smiles between 2 and 18 seconds? .2. Find the 90% percentile for an eight—week old baby’s smiling time. 3. Find the probability that a random eight-week old baby smiles more thanl2 seconds knowing that the
baby smiles more than 8 Seconds. Page 3 of 5 STAT 35000-51130 21325: Homework 4 PROBLEM 4 Problem 4 Assume jobs arrive every 15 seconds on average.
1. Specify an appropriate probability model to model the number of jobs arrived during a given minute. 2. What is the probability to get exactly 4 jobs during a given minute?
3. Specify an appropriate probability model to model the waiting time (in minute) for a job to arrive. 4. What is the probability of waiting less than or equal to 30 seconds, i.e .5 min, to. get a job?
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(as ) r( a U) mrmm€(f’ﬂpojb Verify it by choosing a particular pair of (p, a} and some reasonable (1,6. 2. Given X N N(,u, 02 = 9), and Pr(‘X S 4) = 0.6, what; is y?
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