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Mean or variance of the number of defective (or white) items in a sample drawn without replacement

This type of question, asked 7 times: 28 Jul 2022, 29 Jan 2023, 5 Apr 2024, 6 Apr 2024, 8 Apr 2024, 28 Jan 2025, 4 Apr 2025. All 7 questions below, oldest first.

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  1. Question 1

    28 Jul 2022

    179
    A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let XX be the number of white balls, among the drawn balls. If σ2\sigma^{2} is the variance of XX, then 100σ2100\sigma^{2} is equal to

  2. Question 2

    29 Jan 2023

    80
    Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable XX denote the number of rotten apples. If μ\mu and σ2\sigma^{2} represent mean and variance of XX, respectively, then 10(μ2+σ2)10\left( \mu^{2}+\sigma^{2} \right) is equal to

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  3. Question 3

    5 Apr 2024

    81
    From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable XX denote the number of defective items in the sample. If the variance of XX is σ2\sigma^{2}, then 96σ296\sigma^{2} is equal to

  4. Question 4

    6 Apr 2024

    175
    From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable XX denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of XX is mn\frac{m}{n}, where gcd(m,n)=1gcd(m,n) = 1, then n−mn-m is equal to

  5. Question 5

    8 Apr 2024

    83
    Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables XX and YY respectively denote the number of blue and Yellow balls. If Xˉ\bar{X} and Yˉ\bar{Y} are the means of XX and YY respectively, then 7Xˉ+4Yˉ7\bar{X}+ 4\bar{Y} is equal to

  6. Question 6

    28 Jan 2025

    69
    Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x denote the number of defective oranges, then the variance of xx is :

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  7. Question 7

    4 Apr 2025

    69
    A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is.

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