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Answer the following about the probability distribution.
From a lot of 6 items containing 2 defective items, a sample of 4 items are drawn at random. Let…
From a lot of 6 items containing 2 defective items, a sample of 4 items are drawn at random. Let the random variable $X$ denote the number of defective items in the sample. If the sample is drawn without replacement, find:
(a)[2.0]
The probability distribution of $X$
(b)[2.0]
Mean of $X$
(c)[2.0]
Variance of $X$
Answer
Answer (b)
AI$E(X) = \sum xP(x) = 0 + \frac{8}{15} + \frac{12}{15} = \frac{20}{15} = \frac43$
Final answer: $\frac{4}{3}$
Answer (c)
AI$E(X^2) = 0 + \frac{8}{15} + \frac{24}{15} = \frac{32}{15}$
$\text{Var}(X) = E(X^2) - [E(X)]^2 = \frac{32}{15} - \frac{16}{9} = \frac{96 - 80}{45} = \frac{16}{45}$
Final answer: $\frac{16}{45}$
From ISC 2018 Mathematics Paper 1, question 14.
Check your working with the Probability distribution calculator: find k, the mean, variance and standard deviation of a random variable, with the working table.