Test two integrated circuits one after another. On each test, the possible outcomes are «accept» and «reject». Assume that all circuits are acceptable with the probability 0.9 and the outcomes of successive tests are indepedent. Count the number of acceptible circuits X and the number of successive tests Y before you observe the first reject. Draw a table for $p_{XY}$. Find PMF.
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9. This means that the probability of rejecting a circuit is 0.1. Show more…
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Test two integrated circuits, one after the other. On each test, the possible outcomes are a (accept) and r (reject). Assume that the circuits are acceptable with probability 0.9, and that the outcomes of successive tests are independent. Count the number of acceptable circuits X and the number of successful tests Y BEFORE you observe the first reject. (If both tests are successful, then X = 2, and Y = 2. If the first circuit is bad, then X = 1, Y = 0, etc.). a. What is the sample space for this experiment? b. Draw a tree diagram for this experiment. c. Construct the joint probability distribution from your tree diagram. d. Determine the marginal probabilities from (c). e. Are the elements of (c) independent? f. Find the covariance and the correlation coefficient of the two random variables X and Y.
Sri K.
Kratika B.
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