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Ex 13.4, 9 - Random variable X has probability distribution - Ex 13.4

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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Ex 13.4, 9 The random variable X has a probability distribution P(X) of the following form, where k is some number : P(X) = ๐‘˜, ๐‘–๐‘“ ๐‘ฅ=0๏ทฎ2๐‘˜, ๐‘–๐‘“ ๐‘ฅ=1๏ทฎ3๐‘˜, ๐‘–๐‘“ ๐‘ฅ=2๏ทฎ0, ๐‘œ๐‘กโ„Ž๐‘’๐‘Ÿ๐‘ค๐‘–๐‘ ๐‘’๏ทฏ๏ทฏ (a) Determine the value of k. Making in tabular format Since X is a random variable , its Sum of Probabilities is equal to 1 0๏ทฎ4๏ทฎ๐‘ƒ(๐‘‹)๏ทฏ = 1 P(x = 0) + P(x = 1) + P(x = 2) = 1 k + 2k + 3k = 1 6k = 1 k = ๐Ÿ๏ทฎ๐Ÿ”๏ทฏ Ex 13.4, 9 (b) Find P (X < 2), P (X โ‰ค 2), P(X โ‰ฅ 2). Our probability distribution table is P(X < 2) = P(X = 0) + P(X = 1) = k + 2k = 3k = 3 ร— 1๏ทฎ6๏ทฏ = ๐Ÿ๏ทฎ๐Ÿ๏ทฏ P(X โ‰ค 2) = P(X = 0) + P(X = 1) + P(X = 2) = k + 2k + 3k = 6k = 6 ร— 1๏ทฎ6๏ทฏ = 1 P(X โ‰ฅ 2) = P(X = 2) + P(x = 3) + P(X = 4) + โ€ฆโ€ฆ = 3k + 0 + 0 + โ€ฆโ€ฆโ€ฆ. = 3k = 3 ร— 1๏ทฎ6๏ทฏ = ๐Ÿ๏ทฎ๐Ÿ๏ทฏ

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