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101年 - 101 國立交通大學_碩士班考試入學試題_資訊聯招：線性代數與機率#113290
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題組內容
14. Let the joint probability density function of X and Y be given by
(b) Find the marginal probability density functions of Y. (6 points)
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(a) If X is a normal random variable with parameters μ = 3 and σ2 =16,find P(1＜X＜11).(4 points)
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(b) If 48 random numbers are selected independently from the interval (0, 1),what is the approximate probability that the sum of these numbers is at least 20? (6 points)
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1. Please describe what factors affect the melting point of metal elements, and also rank the melting points of Na, Mg, Al and explain the reasons. [10分]
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(a)原子逐漸接近後,位能高低會如何變化,並請說明理由。
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(b)原子間距離由無窮遠接近到鍵結距離,形成金屬的過程為放熱還是吸熱，並請說明理由。
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3. Draw the cubic crystal plane that intersects the following position coordinates: 1/2, 2/3, 1, and determine the Miller indices of the plane.[10分]
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(a)為何蠟燃燒必須要用火柴點一下，否則在空氣中很久也不會燒起來?
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(b)為何蠟燭點燃後，卻會持續地燃燒?
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(c)請繪製蠟燭燃燒過程的自由能變化?
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5. To improve the physical and chemical properties of metal materials, it is common to introduce heteroatoms into the parent material to form a solid solution during metallurgy. Please describe what types of solid solutions that heteroatoms can form, and describe what factors affect the solubility of these heteroatoms in the solid solutions. [10分]
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101年 - 101 國立交通大學_碩士班考試入學試題_資訊聯招：線性代數與機率#113290
101年 · #113290
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