Question

The number of flaws x on an electroplated automobile grill is known to have the following probability mass function:
p(0) = 0.6; p(1) = 0.2; p(2) = 0.1; p(3) = 0.1
a) Is this random variable continuous or discrete? Justify your answer.
b) Verify that this is a proper mass function
c) What is the probability that a randomly selected grill has fewer than 2 flaws? Calculate the probability, and use proper probability notation.
d) What is the probability that a randomly selected grill has 2 or more flaws? Calculate the probability, and use proper probability notation.
e) What is the probability that a randomly selected grill has exactly 2 flaws? Calculate the probability, and use proper probability notation.

Question 2. The following is a density function for the random variable x that describes the time to failure (in days) of a computer component (the time until the component fails to work).
?(?)=11000?−?1000; x>0
a) Is the random variable x discrete or continuous? Justify your answer.
b) What is the cumulative distribution function (F(x)) for this random variable?
c) What is the probability that the time to failure for this computer component is less than 200 days? Calculate the probability, and use proper probability notation.
d) What is the probability that the time to failure for this computer component ≥ 200 days? (Hint, consider what is the complement of this event). Calculate the probability, and use proper probability notation.

Question 4. Temperature transducers of a certain type are shipped in batches of 50 units. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data:
2 1 2 4 0 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
(a) Determine the frequencies and relative frequencies for the observed values of x, which is the number of nonconforming transducers in a batch.
(b) What proportion of batches in the sample have at most five nonconforming transducers?
Question 5. An experiment to study the lifetime (hr) for a certain type of component involved putting 10 components into operation and observing them for 100 hours. Eight of the components failed during that period, and those lifetimes were recorded. Denote the lifetimes of the two components still functioning after 100 hours by 100+ (these data have been “censored from the right”). The sample observations were:
48, 79, 100+, 35, 92, 85, 57, 17, 100+, 29
a) Which of the measures of center for empirical data can be determined for this experiment (mean, median, mode)? Explain, for each measure of center, why it can or cannot be used.
b) Find the value for any measure of center you believe possible for these data.

Answer 1