Suppose that the random variable x has an exponential distribution with λ = 2. (a) Write the formula for the exponential probability curve of x. What are the possible values of x? 2. for x 2 20¹x (c) Find P(x ≤ 1). (Round your answer to 4 decimal places.) 0.8647 (d) Find P.25 ≤x≤ 1). (Round your answer to 4 decimal places.) AAK o^2x 0.4712 (e) Find Pix 2 2). (Round your answer to 4 decimal places.) 0.0183 (f) Calculate the mean, µ, the variance, o, and the standard deviation, 0, of the exponential distribution of x. (Round your answers to 2 decimal places.)
Suppose that the random variable x has an exponential distribution with λ = 2. (a) Write the formula for the exponential probability curve of x. What are the possible values of x? 2. for x 2 20¹x (c) Find P(x ≤ 1). (Round your answer to 4 decimal places.) 0.8647 (d) Find P.25 ≤x≤ 1). (Round your answer to 4 decimal places.) AAK o^2x 0.4712 (e) Find Pix 2 2). (Round your answer to 4 decimal places.) 0.0183 (f) Calculate the mean, µ, the variance, o, and the standard deviation, 0, of the exponential distribution of x. (Round your answers to 2 decimal places.)
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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 13E
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Transcribed Image Text:Exercise 7.48 (Static) METHODS AND APPLICATIONS
Suppose that the random variable x has an exponential distribution with A = 2.
(a) Write the formula for the exponential probability curve of x. What are the possible values of x?
P
2^x
(c) Find P(x ≤ 1). (Round your answer to 4 decimal places.)
0.8647
(d) Find P(.25 ≤x≤1). (Round your answer to 4 decimal places.)
μX
o^2x
OX
2. for x2
0.4712
(e) Find P(x > 2). (Round your answer to 4 decimal places.)
0.0183
(f) Calculate the mean, the variance, o, and the standard deviation, O, of the exponential distribution of x. (Round your answers
to 2 decimal places.)
(g) Find the probability that x will be in the interval [μ ±20%). (Round your answer to 4 decimal places.)
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