a-1. The rate parameter λ is equal to the reciprocal of the mean. So, λ = 1/0.16 = 6.250.
a-2. The standard deviation of an exponentially distributed random variable is equal to the reciprocal of the rate parameter. So, the standard deviation of X is equal to 1/6.250 = 0.160.
b. To compute P(X > 0.24), we can use the exponential probability density function:
P(X > 0.24) = 1 - P(X ≤ 0.24)
= 1 - (1 - e^(-λx))
= e^(-λx)
= e^(-6.250 * 0.24)
≈ 0.0030 (rounded to 4 decimal places).
c. To compute P(0.09 ≤ X ≤ 0.24), we can again use the exponential probability density function:
P(0.09 ≤ X ≤ 0.24) = P(X > 0.09) - P(X > 0.24)
= e^(-λ * 0.09) - e^(-λ * 0.24)
= e^(-6.250 * 0.09) - e^(-6.250 * 0.24)
≈ 0.0669 (rounded to 4 decimal places).
A random variable X is exponentially distributed with a mean of 0.16.
a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.)
a-2. What is the standard deviation of X? (Round your answer to 2 decimal places.)
b. Compute P(X > 0.24). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
c. Compute P(0.09 ≤ X ≤ 0.24). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
1 answer
1 answer