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Given the exponential distribution: f(x) = {1/θ e^(-x/θ) ; x > 0
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![16. If X has an
exponential distribution, show that
P[(X≥t+T)|(x≥T)] = P(X≥t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F868f8ce6-626d-4ec4-a5d0-0d068fad4c86%2F808cd1be-b37e-4222-9d8d-7df7ebdad75c%2Fqgql8gu_processed.jpeg&w=3840&q=75)
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.Suppose that X has a Poisson distribution with h = 80. Find theprobability P(x is less than or equal to 80)Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.
- Suppose X follows a continuous uniform dis-tribution from 1 to 5. Determine the conditional probabilityP (X > 2.5|X ≤4)If X has an F distribution with ν1 and ν2 degrees offreedom, show that Y = 1Xhas an F distribution with ν2 and ν1 degrees of freedom.2. When using the central limit theorem for means with n = 67, it is not necessary to assume the distribution of the population data is normally distributed. True False
- Suppose that the random variable X is continuous and takes its values uniformly over the interval from 0 to 2. What is P{X = 1.5 or X = 0.4}?Calculate the probability that is between 0.2 and 0.7, if x is uifomly distributed in the interval [0,1]If the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.
- Workers at a large toxic cleanup project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then μ = 7500 andσ ≈ 1750.† A random sample ofn = 70 workersfrom the toxic cleanup site were given a blood test that showedx = 6920.What is the probability that, for healthy adults,xwill be this low or lower?(a) How does the central limit theorem apply? Explain. The central limit theorem describes the distribution of x as normal with mean μ x = 7500 and σ x≈1750.0.The central limit theorem describes the distribution of x as normal with mean μ x = 7500 and σ x≈209.2. The central limit theorem does not apply because the sample size is too small.The central limit theorem describes the distribution of x as normal with mean μ x = 7500 and σ x≈25.0. (b) ComputeP(x ≤ 6920).(Round your answer to four decimal places.) P(x ≤ 6920)= (c) Based on your answer to…Suppose one randomly chooses a values X on the interval (0, 2), and then random choosing a second point Y from 0 to X . Find the probability P ( X + Y > 2 ) .Suppose that X has a continuous uniform distribution between 0 and 20. What is the probability that x is between 0 and 5?