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A continuous random variable X has a probability density function f(x) = e-x , 0 < x < ∞, Then P{X > 1 } is
  • a)
    0.368
  • b)
    0.5
  • c)
    0.632
  • d)
    1.0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A continuous random variable X has a probability density function f(x)...
To find the probability that X is greater than 1, we need to integrate the probability density function f(x) from 1 to infinity:

P(X > 1) = ∫1∞ e-x dx

Using integration by substitution, let u = x and du = dx:

P(X > 1) = ∫e-udu, where the limits of integration are from u = 1 to u = infinity

P(X > 1) = [-e-u]1∞

P(X > 1) = (-e-∞) - (-e-1)

Since e-∞ is equal to zero, we can simplify the expression:

P(X > 1) = e-1 ≈ 0.368

Therefore, the probability that X is greater than 1 is approximately 0.368.
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Community Answer
A continuous random variable X has a probability density function f(x)...
1- int(limits 0 to 1) e-x
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A continuous random variable X has a probability density function f(x) = e-x, 0 < x < ∞, Then P{X > 1 } isa)0.368b)0.5c)0.632d)1.0Correct answer is option 'A'. Can you explain this answer?
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