A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is (ka f(z) = 0<ょく2 otherwise a Find the value of k and draw the corresponding density curve. [Hint: Total area under the graph of f(z) is 1.] ANSWER b. What is the probability that the lecture ends within1 min of the end of the hour? ANSWER I c. What is the probability that the lecture continues beyond the hour for between 60 and 90 sec? ANSWER I d. What is the probability that the lecture continues for at least 90 sec beyond the end of the hour? ANSWER I
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is
kx?
0 < x < 2
f(x):
otherwise
a. Find the value of k and draw the corresponding density curve. [Hint: Total area under the graph of f(x) is 1.]
ANSWER I
b. What is the probability that the lecture ends within 1 min of the end of the hour?
ANSWER I
c. What is the probability that the lecture continues beyond the hour for between 60 and 90 sec?
ANSWER I
d. What is the probability that the lecture continues for at least 90 sec beyond the end of the hour?
ANSWER I](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbeeb476-a64f-4459-b8af-acf5dbdffec4%2F6a88ffbd-f927-462b-86b7-b904a8d73780%2Fgyf2rxm_processed.png&w=3840&q=75)
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