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Need help with exponential random variable question

Statistics
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Suppose that an electronic device has a life length X (in units of 1000 hours) which is considered as an exponential random variable with probability density function f(x) = e^-x , x > 0. Suppose that the cost of manufacturing one such item is $2.00. The manufacturer sells the item for $5.00, but guarantees a total refund if X ≤ .90. What is the manufacturer’s expected profit per item?

Apr 26th, 2015

X follows exponential with probability density function f(x) = e^-x ,   x > 0 (in 1000 hours)

Manufacturer refunds (makes loss of $2 that is profit of -$2) if X <= 0.9

P (X <= 0.9) = 0.593 (using excel and CDF of exponential distribution as 1-exp(-0.9) )

So he will make loss of $2 with probability 0.593 and profit $3 ($5-$2 = $3) with probability 1-0.593

So expected profit is 0.593*(-$2) + (1-0.593)*$3 = $0.033 per item.


Apr 27th, 2015

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