Suppose there are 8 lightbulbs, 5 of which are bad, in a box. If the light bulbs are chosen at random, what is the probability that: a) the first three you chose are all good? b) at least one of the first three is good? c) you must pick four bulbs to find one that is good?

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A: The pdf is

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A: Let Y has gamma distribution with α=n/2 Define W=2Y/β has χ2 with n degree of freedom

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A: The given information is as follows:The  be independent random variable each uniformly distributed…

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A: The PDF is given as follows:

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A: The given information is:Total number of CDs owned: 23Number of CDs to be arranged in the CD rack:…

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A: We know that There are 52 cards in the deck divided into two colour i.e red(26) and black (26).…

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A: Range of the sampling distribution is smaller than the range of the original population .

Q: 7.33. If E[X] = 1 and Var(X) = 5, find (a) E[(2 + X)²]; (b) Var (4 + 3X).

A: E(X)=1,V(X)=5

Q: got 563,320 answer choice D what I am doing wrong. I did E(X) = 0.59 x 624 + 0.41 x 476 = 563.32

A: The payoffs (in thousands of dollars), probabilities, and decision trees are provided

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A: The given table shows the distribution of cars in a household: 00.0210.1820.6030.1540.05

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A: From the provided information,Confidence level = 99%

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A:

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A: The density function fX(x) can be obtained by differentiating the CDF FX(x).

Q: A pdf is defined by : f (x, y) = [ C (x + ay) if 0<y<1 0<x<2 Lo осусі otherwise (A) find the value…

A: The joint PDF of the random variables  and  is given as follows:

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A:

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A: The random variables  and  have the joint probability density function   given as,

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A:

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A: Sample size(n)=15Sample mean x¯=195Sample standard deviation (s)=2.3Population mean μ=200Claim:…