4. Suppose X has a standard normal distribution. Then E(X) = 0 and Var(X) = 1, so...
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4. Suppose X has a standard normal distribution. Then E(X) = 0 and Var(X) = 1, so E(X2) = 1. So
∞ 1 1 = √ x2 2 ∞
−x 2 e 2/2dx = √ x e−x2/2dx.
2π −∞ 2π 0 Substitute y = x2/2 in this integral to evaluate Γ(3/2).
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I am a graduate of Chemistry and also a registered chemist in my country. I have heavy exposure with petroleum, inorganic, organic and analytical chemistry—all being tied to my work experience in the petrochemical industry. Part of my undergraduate coursework was to prepare lessons and lesson plan and to get to teach a whole class using different teaching approaches to ensure that learning was interactive and insightful and more importantly drive home the topic. I also experienced handling peer review groups, still with chemistry as well as one-on-one tutoring with junior high students. When preparing for the tutoring, I always make sure to cover as many references as I can for the topic, then try to create a summary and outline so the lesson would be compact, without missing the salient points. I would give them challenge questions every now and then to try and gauge my students’ understanding—whether we should continue on with the topic or I’d try and expound more, slow down, rest, give more concrete and relatable examples and see to it they learn with me. Especially with chemistry, when it is involved in every aspect of our daily lives. No matter how minute and mundane a task/object is, we appreciate its beauty and importance by viewing its chemical background and origins.
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