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STAT 101 UIC Probability Distribution True and False Questions

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Key Assignment-2 (STAT-101) 2019-20 IInd Semester True and False Questions 1. The following Table describes a probability distribution. x P(x) 0 0.10 1 0.15 2 0.50 3 0.30 Ans: False Hint: ∑ 𝑃(𝑥) = 0.10 + 0.15 + 0.50 + 0.30 = 1.05 ≠ 1 The requirement ∑ 𝑃(𝑥) = 1 is not satisfied so above Table does not describe a prob. distribution. 2. The random variable X has the following probability distribution. x 0 P(x) k The value of k is 0.10. 1 3k 2 6k Ans: True Hint: ∑ 𝑃(𝑥) = 1 i.e. k + 3k + 6k =1 so k = 1 10 = 0.10 3. The random variable X has the following probability distribution. x P(x) 0 0.25 1 0.25 2 0.50 The mean of this distribution is 1.25 Ans: True Hint: Mean, 𝜇 = ∑[𝑥 • 𝑃(𝑥)] = 0 × 0.25 + 1 × 0.25 + 2 × 0.50 = 1.25 1 4. A coin is tossed 4 times. The probability of getting Head exactly 3 times is 4 × ( )4 . 2 Ans: True 1 1 Hint: In usual notation, 𝑛 = 4 , 𝑝 = and so 𝑞 = 1 − 𝑝 = ; 𝑥 = 3 2 2 Using binomial distribution formula, 𝑛! 𝑃(𝑥) = 𝑝 𝑥 𝑞 𝑛−𝑥 (𝑛 − 𝑥)! 𝑥! 4! 1 3 1 4−3 2 2 𝑃(3) = (4−3)!3! ( ) ( ) = 4! 1!3! 1 3 1 1 2 2 2 ( ) ( ) = 4 × ( )4 5. If the z – score of normal distribution is –2, the mean of the distribution is 20 and the standard deviation of normal distribution is 2.5, then the value of X for a normal distribution is 15. Ans: True 𝑋−𝜇 Hint: 𝑧 = ⟹ 𝑋 = 𝜇 + 𝑧𝜎 = 20 + (−2)(2.5) = 15 𝜎 6. The a ...
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