Topic04 - which can be calculated based on Z-table 4.4 Two types of problems related to normal distribution a Find probability i.e P(X>10)=

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Topic 4 Distribution of Continuous Random Variable 4.1 Uniform distribution : If c and d are numbers on the real line ( c < d ), the probability curve describing the uniform distribution on [c, d] is The probability that x is any value between the given values a and b ( a < b ) is Where c < a < b < d 4.2 Normal Distribution : The density function is 2 μ )/ σ ] (1 /2 )[(X e 2 π 1 f(X ) = σ We denote it as N( μ , σ 2 ) 4.3 Standardization of Normal Random Variable X~ N( μ , σ 2 ) then is standardized normal random variable, N(0,1) () d x c c d = x for 1 f () c d a b b x a P = 12 ) ( 2 2 2 c d d c X X = + = μ = X z
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To find probability P(a<X<b) it is equivalent to find
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Unformatted text preview: which can be calculated based on Z-table 4.4 Two types of problems related to normal distribution a. Find probability , i.e P(X>10)=? Where X-N(10,100) b. Find limit boundary: i.e. P(X>a)=95% , find a . An important application in finance is to find Value at Risk (VaR) . In the example above, “a” is VaR at the level of 95% . If X denote the firm cashflow, it implies the firm value will exceed “a” with probability of 95% ) ( σ μ − < < − b z a P...
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This note was uploaded on 09/15/2008 for the course ISMT 111 taught by Professor Wanxuhu during the Fall '08 term at HKUST.

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Topic04 - which can be calculated based on Z-table 4.4 Two types of problems related to normal distribution a Find probability i.e P(X>10)=

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