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11.1. 13.2. 0.3. 12.4. (2.5. Construct the probability distribution based on the following frequency distribution: OUTCOMES: 102 105 103 111 114 117 FREQUENCIES: 10 20 45 15 20 15 {3) Draw the Histogram graph of the probability distribution. [b] Compute the expected value of the outcomes. {:1 Compute the Variance and Standard Deviation of the probability distribution. A coin is biased such that a HEAD is three times as likely to occurs as a TAIL. Find the expected TAILS when this coin is tossed thrice. Let x be the random Variable with the following probability distribution: X: 3 6 9 P{X): 1m 112 us [a] Compute EDI). (d) Compute E[1/2[5x - 7)] [b] Compute [2012) [e] Compute 15(5): - 13]2 [c] Compute [2(1me [1] Compute apt + 112 Let x be the random variable and has the following probability distribution: 1:: 1 5 9 P111]: A B c Where A. B. C are any constants. It is also known that PGC 4] and P{X s 5] = 2P[K :- 5]. Find the values ofA, B and C. Find the value of R such that the following are the probability distributions: [a] For) = K/xa where x = 1, z, 3, 4 [b] Put] = xx2 where x = 0.5. 025,0.75 Also Compute the Mean and Varianoe of the above distributions