LEC11a M & Var Func of Disc rv

# LEC11a M & Var Func of Disc rv - FUNCTION OF A DISCRETE...

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FUNCTION OF A DISCRETE R.V. r.v. X= number of defects on a part. Here is prob dist of X: x 0 1 2 f(x) .3 .5 .2 In each example, r.v. C = cost Give function c=h(x) and prob dist of C. Ex) The cost per unit is \$2 per defect. Ex) The cost is \$3 to check a unit plus \$2 per defect to repair. Ex) The cost to repair defects (if there is at least 1) is \$5 per defect plus a fixed cost of \$3.

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The cost to repair defects (if there is at least one) is \$5 per defect plus a fixed cost of \$3. Give C as a function of X. Give pdf of C. Find the mean and variance of cost. r.v. X = number of defects r.v. C = cost of defects x 0 1 2 f(x) .3 .5 .2 C C 2 E( C ) = E( C 2 ) = V( C) = SD(C) 2
Mean of a Function of a Random Variable: A r.v. X has pdf f(x) and possible values x 1 , x 2 , . .. If h(X) is any function of the r.v. X, then E h X h x f x h x P X x i i i i i i ( ( )) ( ) ( ) ( ) ( ) = = = . 3

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Example The distance to a fire is 1 or 2 miles with probability 0.7 or 0.3. The cost to travel to the fire is 5 + 2X, and the time to travel is
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LEC11a M & Var Func of Disc rv - FUNCTION OF A DISCRETE...

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