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0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 nr0.1 16 0 0.1853 0.028 0.0100 0.0033 0.000

ID: 3052056 • Letter: 0

Question

0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 nr0.1 16 0 0.1853 0.028 0.0100 0.0033 0.0003 0.0000 1 0.5147 0.1407 0.0635 0.0261 0.0033 0.0003 0.0000 2 0.7892 0.3518 0.197 009 0.0183 0.002 0.0001 3 0.9316 0.5981 0.4050 0.2459 0.0651 0.0106 0.0009 0.0000 4 0.9830 0.7982 0.6302 0.4499 0.1666 0.0384 0.0049 0.0003 5 0.9967 0.9183 0.8103 0.6598 0.3288 0.10 0.0191 0.0016 0.0000 6 0.9995 0.9733 0.9204 0.8247 0.5272 0.2272 0.0583 0.0071 0.0002 7 0.9999 0.9930 0.9729 0.9256 0.7161 0.4018 0.1423 0.0257 0.0015 0.0000 8 1.0000 0.9985 0.9925 0.9743 0.8577 0.5982 0.2839 0.0744 0.0070 0.0001 0.9998 0.998 0.9929 0.9417 0.7728 0.4728 0.1753 0.0267 0.0005 1.0000 0.9997 0.9984 0.9809 0.8949 0.6712 0.3402 0.0817 0.0033 0000 0.9997 0.995 09616 0.8334 0.5501 0.2018 0.017o 0000 0999 0.989 0.9349 0.754 0.4019 0.0684 0.9999 0.9979 0.98170.9006 0.6482 0.2108 1.0000 0.9997 0.9967 0.9739 0.8593 0.4853 .0000 0.9997 0.9967 0.9719 0.8147 1.0000 1.0000 1.0000 1.0000 10 12 13 14 15 16 7. Let X Bin(16, 0.4). Use the table of cumulative probabilities above to find probabilities related to X. Use proper probability notation in terms of r.v. X for all questions involving a probability. a. Find the probability that X will be less than or equal to 7 b. Find the probability that X will be strictly greater than 6. c. Find the probability that X will be at least 5 but not more than 9. d. Calculate the mean and variance of X

Explanation / Answer

7) a) P(X < 7 ) = 0.7161

b) P(X > 6) = 1 - P(X < 6)

                   = 1 - 0.5272

                   = 0.4728

c) P(5 < X < 9)

= 0.9417 - 0.1666

= 0.7751

d) mean = n * p = 16 * 0.4 = 6.4

variance = n * p * (1 - p)

               = 16 * 0.4 * 0.6 = 3.84