Question

Four-week summer rainfall totals, in inches, in a section of the Midwestern United States have approximately a gamma distribution with α = 1.8 and β = 5. (a) Find the mean, in inches, and variance of the four-week rainfall totals. E(X) = 9 inches V(X) = 45 inches (b) What is the probability that the four-week rainfall total exceeds 7 inches? (Round your answer to four decimal places.)

Name: four week summer rainfall totals in inches in a section of the midwestern united states have approximately a gamma distribution with 18 and 5 a find the mean in inches and variance of the fo 53815
Uploaded: 2023-04-03T16:25:11-08:00
Duration: 1 min 57 s
Channel: James Kiss
Description: four week summer rainfall totals in inches in a section of the midwestern united states have approximately a gamma distribution with 18 and 5 a find the mean in inches and variance of the fo 53815

          Four-week summer rainfall totals, in inches, in a section of the Midwestern United States have approximately a gamma distribution with α = 1.8 and β = 5.

(a) Find the mean, in inches, and variance of the four-week rainfall totals.
E(X) = 9 inches
V(X) = 45 inches

(b) What is the probability that the four-week rainfall total exceeds 7 inches? (Round your answer to four decimal places.)

Added by John P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert James Kiss

04/03/2023

Step 1

Given: Alpha (α) = 1.8 Beta (β) = 5 X = 7 Using the gamma distribution formula: \[ P(X > 7) = 1 - \frac{\beta^\alpha}{\Gamma(\alpha)} \int_{0}^{7} x^{\alpha-1} e^{-\beta x} dx \] Show more…

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Four-week summer rainfall totals, in inches, in a section of the Midwestern United States have approximately a gamma distribution with α = 1.8 and β = 5. (a) Find the mean, in inches, and variance of the four-week rainfall totals. E(X) = 9 inches V(X) = 45 inches (b) What is the probability that the four-week rainfall total exceeds 7 inches? (Round your answer to four decimal places.)