Construct the cumulative distribution function (cdf) of X. (6 points) 2. The out

Question

Construct the cumulative distribution function (cdf) of X. (6 points)

2.The output of a chemical process is continually monitored to ensure that the concentration remains within acceptable limits. Whenever the concentration drifts outside the limits, the process is shut down and recalibrated. Let X be the number of times in a given week that the process is recalibrated. The following table presents values of the probability mass function (pmf) f(x).

(a).Find the probability that the process is recalibrated fewer than two times during a week. Enter your final answer as a decimal without rounding. (5 points)

(b)Find the probability that the process is recalibrated more than three times during a week. Enter your final answer as a decimal without rounding. (2 points)

The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in uninterrupted rolls of uniform width, is given by* 20 30 4P foc) 0.41 0.37 0.16 0.05 0.01e

Explanation / Answer

Question 1:

The CDF for the given probability density distribution is computed as:

Question 2:

a) Now the probability that the process is recalibrated fewer than 2 times during the week is computed as:

P(X < 2) = P(X=0) + P(X=1) = 0.17 + 0.36 = 0.53

Therefore 0.53 is the required probability here.

b) Probability that the process is recalibrated more than three times during a week is computed as:

P(X > 3) = P(X=4) = 0.03

Therefore 0.03 is the required probability here.

X F(X=x) 0 0.41 1 0.41 + 0.37 = 0.78 2 0.78 + 0.16 = 0.94 3 0.94 + 0.05 = 0.99 4 0.99 + 0.01 = 1

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