let X be a random variable following an exponential distribution with parameter 1-0 with the density function f(x) = 2^x, for x>0 f(x) = 0 elsewhere. (a) How do you derive the distribution Y = 10-e-^x ? дал (6) How do you derive the moment generating function of y (c) Hf X₁, X₂, X₂...... X₁. are random sample from the previous exponential distribution with parameter x>0 (Xi's (i=1,2,..., 10 ) are independent). Flow de the density function of 7 = min{X₁, X₂, X₁0 3. P(272) = PIX, >2,.... X ₁ > 2). you find 10

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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let X be a random variable following an exponential
distribution with parameter 1³0 with the density
function f(x) = 2 e²^x, for x>0 f(x) = 0, elsewhere.
(a) How do you derive the distribution Y = 10-e-^x ?
(b) How do you derive the moment generating function of y
(c) If X₁, X₂ X3...... X₁. are random sample from the
previous exponential distribution with parameter 20
(X;'s (i = 1, 2,...,10 ) are independent). Flow do you find
the density function of Z= min{X₁, X₂,
P(Z > 2) = PIX₁ > 2,.... X₁₁ > 2)
X₁0 3.
サ
'21''' L
Transcribed Image Text:let X be a random variable following an exponential distribution with parameter 1³0 with the density function f(x) = 2 e²^x, for x>0 f(x) = 0, elsewhere. (a) How do you derive the distribution Y = 10-e-^x ? (b) How do you derive the moment generating function of y (c) If X₁, X₂ X3...... X₁. are random sample from the previous exponential distribution with parameter 20 (X;'s (i = 1, 2,...,10 ) are independent). Flow do you find the density function of Z= min{X₁, X₂, P(Z > 2) = PIX₁ > 2,.... X₁₁ > 2) X₁0 3. サ '21''' L
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