Question

5. Suppose a baseball player hits a "single” twice as likely as a "double”, which is twice as likely as a "triple”, which is as likely as a "home run”. Also, his batting average (the probability that he gets a hit) is 0.3. Let B denote the number of bases touched safely during an at-bat. For example, B=0 for out, B = 1 for a single, and so on. (a) Find the PMF of B. (b) Find the CDF of B. (c) Draw the CDF

Answer 1

Theory: - PDF , (Probability is a statistical experssim a probability distribution for random variable Density functions) that defesses a discrete The CDF ( commulative Distol bation function of Random variable x is defined as F(x= x) = P(XŞx) for all str. . Now leto assume if baseball is Mit Probability of single is ? so Probability of double = / ( half of single) Probability of Toiple = 1/2) = 2 (half of Doubt Bobability of Home run= b (equal to Triple Poobability of Not Hit P(B=0) = 0.7 so Pro bability of reit - Aus P (1360) =0.3

| PB-1) + P(k-) + R (K=J) + R(B=4) = 0.3 P 15 10.075 이명 이 c. 031S R.D.F Ple) 0 10.15 1. 13 01-23 | 나. 0.01S OIS 0.037S Total

Now F C.D. Flx )= P(X£ x) P(B40) = P(8=0) = 0-7 PCBL 12 ple=0) +P18=3) = 0.7 + 0.15 = 0.85 p(342) = P(B-0)+ P(6-1) +P (639) . o. 7 to 15 +0.075 = 0.925 P(BL) = P(BL2) + P(B=3) . 0.9695 so P(B24)= P(BL 3) + P(B-4) 24 P (B<x] 0.30 0.85 0.925 0.9695 C.D.F - Table

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