# chp5 - Ch5 Continuous Random Variables...

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1 Ch5 Continuous Random Variables Homework:1,11,15,18,19,21,31,39, 40,72,76,79,81,95,101

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2 Sec 5.1: Continuous Distributions We will discuss three popular continuous distributions, the uniform distribution , the normal distribution and the exponential distribution in this chapter. We will not discuss the topic of approximating a binomial distribution with a normal distribution because it is no longer an important issue.
3 Sec 5.2: The Uniform Distribution A continuous random variable that has equal likely outcomes over it entire range of possible values possesses an uniform distribution. Suppose that the random variable x can assume values only in the interval c < x < d. Then the probability density function of x is p x d c ifc x d ( ) . = - 1

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4 The expectation, the variance, and the standard deviation of x are and respectively. ( 29 μ σ = + = - d c d c 2 12 2 2 , ( 29 σ = - d c 2 12
5 <Example 5.1>: (Basic) Suppose x is a uniform random variable with c = 1 and d = 9. (a) Find the probability density function of x. (b) Find the mean, variance, and standard deviation of x. (c) Compute P(x > 2). (d) Compute the probability P( μ - σ < x < μ + σ29. (e) Compute the probability P( μ -2 σ < x < μ +2 σ29. <Solutions>:

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<Example 5.2>: X is a uniformly distributed random variable in the interval (1 , 11). (a) Find the probability density function of X. (b) Find mean and standard deviation of X. (c) Find s such that P(X > s) = 0.7.
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chp5 - Ch5 Continuous Random Variables...

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