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Unformatted text preview: X , f ( ) 0, x be x x x& ≥ ± = ² < ± ³ Note: The first step is to find the value of b . 5. Let X be an exponential random variable with parameter ± . a. For x > 0, find P({X & x }). b. For x 2 > x 1 > 0, find P({ x 1 & X & x 2 }). c. For x > 0, find P({X ² x }). d. Segment the positive real line into three equiprobable disjoint intervals. 6. The random variable X is N(10,1). Find f X ( x  (X10) 2 <4). 7. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by ± ³ ± ² & ≤ > = 10 10 10 ) f( 2 x x x x What is the probability that of 6 such devices at least 3 will function for at least 15 hours? You may assume that the functioning of each device is independent of the functioning of the other devices....
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 Fall '08
 Staff
 Probability theory, probability density function, Cumulative distribution function, cdf FX

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