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Suppose that random variables X, and X₂ have exponential distribution with expected value of and respectively. Assume that X₁ and X₂ are independent of each other. Find i) The joint density function of X₁ and X₂. ii) P(X₂ >1, X₂ > 1) iii) P(X₂ <5) A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by

Suppose that random variables X, and X₂ have exponential distribution with expected value of and respectively. Assume that X₁ and X₂ are independent of each other. Find i) The joint density function of X₁ and X₂. ii) P(X₂ >1, X₂ > 1) iii) P(X₂ <5) A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 30CR
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f(y) = ye to 100' 0 <y<∞ elsewhere 0, Derive the expected value of Y? O Suppose that a random variable Y is uniformly distributed on an interval (0,1) and let c> 0 be a constant. i) Find the moment generating function of X = -cY. ii) What is the distribution of X?
Transcribed Image Text:f(y) = ye to 100' 0 <y<∞ elsewhere 0, Derive the expected value of Y? O Suppose that a random variable Y is uniformly distributed on an interval (0,1) and let c> 0 be a constant. i) Find the moment generating function of X = -cY. ii) What is the distribution of X?
Suppose that random variables X₁ and X₂ have exponential distribution with expected value of and respectively. Assume that X₁ and X₂ are independent of each other. Find i) The joint density function of X₁ and X₂. ii) P(X₁ >1, X₂ > 1) iii) P(X₂ <5) A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by
Transcribed Image Text:Suppose that random variables X₁ and X₂ have exponential distribution with expected value of and respectively. Assume that X₁ and X₂ are independent of each other. Find i) The joint density function of X₁ and X₂. ii) P(X₁ >1, X₂ > 1) iii) P(X₂ <5) A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by
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