7. Suppose that there are two service stations in a country town, Alan Auto and Geoff’s Garage and that from month to month:
●the probability that a customer will stay at Alan’s Auto is 0.8, otherwise they will move to Geoff’s Garage, andthe probability that a customer will stay with Geoff’s Garage is 0.9, otherwise they will move to Alan’s Auto.
●Initially, Alan’s Auto has x customers and Geoff’s Garage has y customers, and the total number of customers is assumed to remain constant.
a. This information is represented in the transition matrix
(2 marks)
b. The expected number of customers at Alan’s Auto at the end of month 1 is:
(2 marks)
c. The expected number of customers Alan’s Auto would have in the long term is
(2 marks)
6. Suppose that the probability of a basketball player scoring a goal is 0.62 if she has scored the preceding goal and 0.33 if she has missed the preceding point.
a. Find the probability that she goals at the fourth attempt if she has missed the first goal .
(2 marks)
b. Find the steady state probability that she scores a goal on a particular attempt.
(2 marks)
c. The probability that the player misses three more goals in a row after missing the first goal, and find scores the next goal.
(2 marks)
5. In a particular country it has been found that the probability of snow is dependent on whether or not it snowed the day before. If it snows one day then the probability of snow the next day is 0.72. If it doesn’t snow one day then the probability of snow on the next day is only 0.08.
a. A transition matrix T that can be used to represent this information,find the T
(2 marks)
b.If it snows on Monday, find the probability that it will snow on Friday can be found .
(2 marks)
c.For this Markov chain, the long term probability of snow, is equal to:
(2 marks)
4.A Markov chain is defined by a
transition matrix T = and an initial
state matrix S0 =
a. For this Markov chain,find S1 .
(2 marks)
b. For this Markov chain,find S2.
(2 marks)
c. For this Markov chain, S10 can be found by evaluating
A .S5× S5 B. T2 × S8 C. S9 × T D. T9 × S0 E. T10 × S1
(2 marks)
d. For this Markov chain, the steady state solution is closest to?
(2 marks)
3. Suppose that a four-state Markov chain is defined by a transition matrix T and an initial state matrix S0. Which of the following is a true statement?
A The dimension of T is 3 × 3 and the dimension of S0 is 3 × 1.
B The dimension of T is 4 × 2 and the dimension of S0 is 4 × 2.
C The dimension of T is 4 × 2 and the dimension of S0 is 4 × 1.
D The dimension of T is 4 × 4 and the dimension of S0 is 4 × 4.
E The dimension of T is 4 × 4 and the dimension of S0 is 4 × 1.
(2 marks)
2. Consider the matrices:
The matrices that could be initial state matrices for a Markov chain are:
A. U only B .V only C .W only D .V and W E. U, V and W
(2 marks)
1.Suppose:
Find the Pr(B2).
(2 marks)
(二)蛋白质的多样性
1、蛋白质结构的多样性
(1)氨基酸的种类不同,构成的肽链不同。
(2)氨基酸的数目不同,构成的肽链不同。
(3)氨基酸的排列顺序不同,构成的肽链不同。
(4)肽链的数目和空间结构不同,构成的蛋白质不同。
两个蛋白质分子结构不同,则这两个蛋白质不是同种蛋白质。但并不是以上这四点同时具备才能确定两个蛋白质分子结构不同,而是只要具备以上其中的一点,这两个蛋白质的分子结构就不同。
2、蛋白质功能的多样性
蛋白质结构的多样性决定了蛋白质功能的多样性。
蛋白质据功能分为结构蛋白和功能蛋白两大类,前者如人和动物的肌肉。后者如具有催化作用的绝大多数酶,具有免疫功能的抗体等。
[思考感悟]许多蛋白质分子中含有-S-S-,它是如何形成的?
-S-S-的形成是由两个-SH基团通过脱去一分子氢形成的。
[基础训练]
1、下列有关蛋白质结构、功能多样性的说法正确的是( C )
A、蛋白质结构的多样性与构成蛋白质的氨基酸的种类、数目和空间结构有关
B、已知某化合物具有催化功能,可以推断此物质为蛋白质
C、有些蛋白质具有防御功能,如抗体;有些蛋白质具有接受信息的功能,如受体。抗体与受体都具有专一性
D、蛋白质空间结构改变,不会影响其生物活性
2、a、b、c表示生物体内的三个生理过程,如图所示的三过程中Y代表的物质和特征分别是( C )
①酶;②抗体;③载体;④选择性;⑤特异性;⑥专一性。
A、①②③;④⑤⑥ B、②③①;⑤④⑥
C、③①②;④⑥⑤ D、③②①;⑥④⑤
3、如图表示人体内几种化学元素和化合物的相互关系,其中a、b表示有机小分子物质,A、B、X代表有机高分子物质,虚线表示遗传信息的流动方向。请据图分析回答 :
(1)a为脱氧核苷酸,共有4种,b的分子结构简式可表示为
。
(2)B可分为B1、B2、B3等,其原因是:从b分析是由于氨基酸的种类、数目和排列次序的不同;从A分析是因为DNA分子结构具有多样性(不同的基因控制合成的蛋白质不同)。
(3)X代表RNA,其彻底水解产物是核糖、磷酸和4种碱基(A、G、C、U)。
(4)B3是由574个氨基酸,四条肽链组成的,在形成1分子B3的过程中,共脱去570分子水。
[高考模拟]
4、(2008海南生物8)关于动物细胞内蛋白质合成与去向的叙述,正确的是( A )
A、所有蛋白质的合成都需要能量 B、合成的蛋白质都运到细胞外
C、合成的蛋白质都不能进入细胞核内 D、合成的蛋白质都用于细胞膜蛋白的更新
5、(2008青岛模拟)下面是某蛋白质的肽链结构示意图(图1,其中数字为氨基酸序号)及部分肽链放大图(图2),请据图判断下列叙述中不正确的是( B )
A、该蛋白质中含有两条肽链49个肽键
B、图2中含有的R基是①②④⑥⑧
C、从图2可推知该蛋白质至少含有4个游离的羧基
D、控制该蛋白质合成的mRNA中至少含有51个密码子
[作业]
(一)蛋白质的分子结构
1、形成:氨基酸 多肽(肽链) 蛋白质。
2、蛋白质与多肽的关系:每个蛋白质分子可以由1条多肽链组成,也可由几条肽链通过一定的化学键(肯定不是肽键)连接而成。但多肽只有折叠成特定的空间结构进而构成蛋白质时,才能执行特定的生理功能。
(五)免疫功能:如人体内的抗体。
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