(a) What is the mean and variance of the price at time t = 4? SOLUTION: E(X(4)) = E(1 + 2B(4) + 20) = 21 + 2E(B(4)) = 21 + 0 = 21. V ar(X(4)) = V ar(1 + 2B(4) + 20) = V ar(2(B(4)) = 4V ar(B(4)) = 42 = 16. (b) What is the probability that at time t = 4, the price is > 14? SOLUTION: X(4) > 14 if and only if 21 + 2B(4) > 14. 2B(4) is N(0, 16) hence can be re-written as 4Z, where Z ∼ N (0, 1). Thus we want P (21 + 4Z > 14) = P (Z > −(7/4)) = P (Z > −1.75) = P (Z ≤ 1.75) = Φ(1.75) = 0.96. (c) Given that the price is 5.5 at time t = 6, what is the probability that the price is > 8 at time t = 7? SOLUTION: X(7) = X(6)+(X(7)−X(6)) = 5.5+(5+2(B(7)−B(6)) = 10.5+2(B(7)−B(6)). By stationary and independent increments, this has the same distribution as 10.5+2B(1) which has the same distribution as 10.5 + 2Z, where Z ∼ N (0, 1). So we want P (10.5 + 2Z > 8) = P (Z > −1.25) = P (Z ≤ 1.25) = Φ(1.25) = 0.89. (d) What is the probability the price goes up to 4 before down to 1/4? SOLUTION: X(t) = 1 + 2B(t) + 5t hits 4 before 1/4 if and only if 2B(t) + 5t hits a = 3 before −b = −3/4. With μ = 5 and σ = 2 we get 2μ/σ2 = (2× 5)/4 = 2.5.
(a)时间t = 4时价格的均值和方差是多少?解决方案:E (X (4)) = E (1 + 2 B (4) + 20) = 21 + 2 E (B)(4) = 21 + 0 = 21。V ar (X (4)) = V ar (1 + 2 B (4) + 20) = V ar (2 (B) (4)) = 4 V ar (B)(4) = 42 = 16。(b)在时间t = 4时，价格> 14的概率是多少?解:当且仅当21 + 2B(4) > 14, X(4) > 14。2B(4)是N(0,16)，因此可以重写为4Z，其中Z ~ N(0,1)。因此我们希望P (21 + 4Z > 14) = P (Z >−(7/4))= P (Z >−1.75)= P (Z≤1.75)= Φ(1.75) = 0.96。(c)假设在时间t = 6时价格为5.5，那么在时间t = 7时价格> 8的概率是多少?解决方案:X (7) = X (6) + (X(7)−X (6)) = 5.5 + (5 + 2 (B(7)−B (6)) = 10.5 + 2 (B(7)−B(6))。通过平稳和独立的增量，它具有与10.5+2B(1)相同的分布，它具有与10.5+ 2Z相同的分布，其中Z ~ N(0,1)。因此我们希望P (10.5 + 2Z > 8) = P (Z > - 1.25) = P (Z≤1.25)= Φ(1.25) = 0.89。(d)价格在下降到1/4之前上升到4的概率是多少?解:X(t) = 1 + 2B(t) + 5t在1/4之前命中4当且仅当2B(t) + 5t在−b =−3/4之前命中a = 3。当μ = 5， σ = 2时，我们得到2μ/σ2 = (2× 5)/4 = 2.5。
{"title":"Professor","authors":"Professor Artem R. Oganov, Frsc Mae","doi":"10.32388/d5qc02","DOIUrl":"https://doi.org/10.32388/d5qc02","url":null,"abstract":"(a) What is the mean and variance of the price at time t = 4? SOLUTION: E(X(4)) = E(1 + 2B(4) + 20) = 21 + 2E(B(4)) = 21 + 0 = 21. V ar(X(4)) = V ar(1 + 2B(4) + 20) = V ar(2(B(4)) = 4V ar(B(4)) = 42 = 16. (b) What is the probability that at time t = 4, the price is > 14? SOLUTION: X(4) > 14 if and only if 21 + 2B(4) > 14. 2B(4) is N(0, 16) hence can be re-written as 4Z, where Z ∼ N (0, 1). Thus we want P (21 + 4Z > 14) = P (Z > −(7/4)) = P (Z > −1.75) = P (Z ≤ 1.75) = Φ(1.75) = 0.96. (c) Given that the price is 5.5 at time t = 6, what is the probability that the price is > 8 at time t = 7? SOLUTION: X(7) = X(6)+(X(7)−X(6)) = 5.5+(5+2(B(7)−B(6)) = 10.5+2(B(7)−B(6)). By stationary and independent increments, this has the same distribution as 10.5+2B(1) which has the same distribution as 10.5 + 2Z, where Z ∼ N (0, 1). So we want P (10.5 + 2Z > 8) = P (Z > −1.25) = P (Z ≤ 1.25) = Φ(1.25) = 0.89. (d) What is the probability the price goes up to 4 before down to 1/4? SOLUTION: X(t) = 1 + 2B(t) + 5t hits 4 before 1/4 if and only if 2B(t) + 5t hits a = 3 before −b = −3/4. With μ = 5 and σ = 2 we get 2μ/σ2 = (2× 5)/4 = 2.5.","PeriodicalId":109925,"journal":{"name":"Encyclopedia of Evolutionary Psychological Science","volume":"196 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132718208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-07DOI: 10.5040/9781350049680.ch-002
Chad Parkhill, E. Stephens
{"title":"Heterosexuality","authors":"Chad Parkhill, E. Stephens","doi":"10.5040/9781350049680.ch-002","DOIUrl":"https://doi.org/10.5040/9781350049680.ch-002","url":null,"abstract":"","PeriodicalId":109925,"journal":{"name":"Encyclopedia of Evolutionary Psychological Science","volume":"7 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114093114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Adolescents are the nation's future leaders, so their immediate environment, including their families, schools, and the government, must promote a healthy environment for them both physically and mentally. This is necessary because improving an adolescent's psychological condition is one of the most crucial investments for raising a good generation, but more and more young people are developing psychological disorders. This study employed a pseudo-experiment method of research. The findings of the study in the treatment group, as shown in the "Paired Samples Test" output table above, indicate that the t count negative value is - 45,020. This difference between the average Pre-Test and the average Post-Test is what causes the t count negative value to be negative. A negative t-count may turn positive in this situation. As a result, the computed t-value is 45,020. While in the control group, it is evident from the "Paired Samples Test" output table above that the negative value t count of -7,760 t counts is due to the average Pre-Test value being lower than the average Post-Test value. A negative t-count may turn positive in this situation. Consequently, the computed t value is now -7.760. Despite the fact that both groups have an impact on pre-and post-test results, the outcomes can be seen if there is a sizable difference between the treatment and control groups. This demonstrates that the treatment group receiving mental education achieves greater results than the group not receiving such treatment. Teenagers' pre-test and post-test personal endurance results for each group show this.
{"title":"Emotional","authors":"Eddy Marheni, E. Purnomo, Nina Jermaina, Goesti Sabda, Laksana, Dudi Komaludin, Eliya Pebriyeni, Firunika Intan Cahyani","doi":"10.32388/wayrrb","DOIUrl":"https://doi.org/10.32388/wayrrb","url":null,"abstract":". Adolescents are the nation's future leaders, so their immediate environment, including their families, schools, and the government, must promote a healthy environment for them both physically and mentally. This is necessary because improving an adolescent's psychological condition is one of the most crucial investments for raising a good generation, but more and more young people are developing psychological disorders. This study employed a pseudo-experiment method of research. The findings of the study in the treatment group, as shown in the \"Paired Samples Test\" output table above, indicate that the t count negative value is - 45,020. This difference between the average Pre-Test and the average Post-Test is what causes the t count negative value to be negative. A negative t-count may turn positive in this situation. As a result, the computed t-value is 45,020. While in the control group, it is evident from the \"Paired Samples Test\" output table above that the negative value t count of -7,760 t counts is due to the average Pre-Test value being lower than the average Post-Test value. A negative t-count may turn positive in this situation. Consequently, the computed t value is now -7.760. Despite the fact that both groups have an impact on pre-and post-test results, the outcomes can be seen if there is a sizable difference between the treatment and control groups. This demonstrates that the treatment group receiving mental education achieves greater results than the group not receiving such treatment. Teenagers' pre-test and post-test personal endurance results for each group show this.","PeriodicalId":109925,"journal":{"name":"Encyclopedia of Evolutionary Psychological Science","volume":"2010 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125628992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
“Reward” explores the personality trait of extraversion in the life of Donald Trump. The chapter begins with an evolutionary account of extraversion’s powerful role in human groups, as a personality trait that enables social actors to attract and hold the attention of others. Studied for over 70 years by personality psychologists, extraversion entails social dominance, gregariousness, and the relentless seeking of reward. Donald Trump is one of the most extraverted human beings on the planet today. The chapter traces the development of this trait in Trump’s life and illustrates how it has served Trump well, infusing tremendous energy and primal charisma into many of his social moments, as he moves from one moment to the next in life. Extraversion is one of five broad and basic traits identified by personality psychologists, often called the Big Five.
{"title":"Reward","authors":"D. McAdams","doi":"10.4324/9780203781043-8","DOIUrl":"https://doi.org/10.4324/9780203781043-8","url":null,"abstract":"“Reward” explores the personality trait of extraversion in the life of Donald Trump. The chapter begins with an evolutionary account of extraversion’s powerful role in human groups, as a personality trait that enables social actors to attract and hold the attention of others. Studied for over 70 years by personality psychologists, extraversion entails social dominance, gregariousness, and the relentless seeking of reward. Donald Trump is one of the most extraverted human beings on the planet today. The chapter traces the development of this trait in Trump’s life and illustrates how it has served Trump well, infusing tremendous energy and primal charisma into many of his social moments, as he moves from one moment to the next in life. Extraversion is one of five broad and basic traits identified by personality psychologists, often called the Big Five.","PeriodicalId":109925,"journal":{"name":"Encyclopedia of Evolutionary Psychological Science","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114829845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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