Mr Sepuru, a statistics class representative, during a Wednesday lecture at 11:10decided to let X₁, X2,..., X10 to be the observations from a random sample of size10 from a distribution with density1√2π0,and ask his fellow students to answer the following questions.f(x) =e²₁-00

It is given that Sample size n = 10 And Xi , i = 1, 2,.......10 follows N(0,1)

Answered: i) What is the moment generating…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Here is another infectious disease model. Once a person becomes infected, the time X, in days, until the person becomes infectious (can pass on the disease) can be modeled as a Weibull random variable with density function f(x,α,β) = (α/βα)xα−1e−(x/β)α for 0 ≤ x ≤ ∞ and 0 otherwise with α = 3.7 and β = 7.1α is the shape parameter and β is the scale parameter. Hint: Solve this with the built-in R functions for the Weibull distribution (dweibull(),pweibull(), qweibull()) not f as defined above. Otherwise you may get intermediate values too large to use. For a) and b) the text (and notes) give formulas for the answers. You can calculate from these formulas. Note that these formulas use the gamma function. Γ(α) is the gamma function. In R, there is a built-in function gamma() which calculates this.f) What is the probability that X is > 4?g) What is the probability that X > 4 given that X > 2?h) Calculate the 70th percentile of X

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i) What is the moment generating function of the sample mean? ii) What will be the mean of the sample mean? iii) Show that the variance of the sample mean is 0.1.