Time remaining:
##### Need help with exponential random variable question

label Statistics
account_circle Unassigned
schedule 0 Hours
account_balance_wallet \$5

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 â‰¤ .90. What is the manufacturerâ€™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

...
Apr 26th, 2015
...
Apr 26th, 2015
Sep 24th, 2017
check_circle