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CLABE Statistics
Homework assignment - Problem sheet 4
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1.
James is expecting three checks in the mail, for 20, 26, and 33 euros. Their arrivals are the events
A, B and C which are independent, with respective probabilities 0.90, 0.75 and 0.80. Let X the
random variable representing the total amount received.
(a)
(b)
(c)
(d)
2.
3.
Find the support and the probability mass function of X .
What is the probability that James receives at least 50 euros? And less than 30 euros?
Calculate the expected amount received.
Calculate the variance and the standard deviation of X .
Find c so that the function f (x) = cx2 for x = 1, 2, 3, 4 is a probability mass function. Calculate
the cumulative distribution function F (·) and show that P (1 < X ≤ 3) = F (3) − F (1).
A quality control engineer is in charge of testing whether or not at least 90% of the DVD players
produced by his company conform to specications. To do this, the engineer randomly selects
a batch of 12 DVD players from each day's production. The day's production is acceptable
provided no more than 1 DVD player fails to meet specications. Otherwise, the entire day's
production has to be tested.
(a) What is the probability that the engineer incorrectly passes a day's production as acceptable
if only 80% of the day's DVD players actually conform to specication?
(b) What is the probability that the engineer unnecessarily requires the entire day's production
to be tested if, in fact, exactly 90% of the DVD players conform to specications?
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