2) Suppose that X is a random variable having a probability density function(2) xe ởf(x; B) =Show whether or notce 7, x>00, elsewhere2 ΣΕ, ΧεВ98% Confidence interval for ẞ if a random sample is given by2.4, 4.6, 3.3, 3.1, 4.6, 2.2, 3.8is a pivotal quantity, Explain and if yes construct a

2) Suppose that X is a random variable having a probability density function xét, x>0 ((3²) ₁ - + xe 0, elsewhere f(x; B) = 2 ΣΕ, Χ ß 98% Confidence interval for ß if a random sample is given by 2.4, 4.6, 3.3, 3.1, 4.6, 2.2, 3.8 Show whether or not is a pivotal quantity, Explain and if yes construct a

2) Suppose that X is a random variable having a probability density function xét, x>0 ((3²) ₁ - + xe 0, elsewhere f(x; B) = 2 ΣΕ, Χ ß 98% Confidence interval for ß if a random sample is given by 2.4, 4.6, 3.3, 3.1, 4.6, 2.2, 3.8 Show whether or not is a pivotal quantity, Explain and if yes construct a

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

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Question

2) Suppose that X is a random variable having a probability density function
(2) xe ở
f(x; B) =
Show whether or not
ce 7, x>0
0, elsewhere
2 ΣΕ, Χε
В
98% Confidence interval for ẞ if a random sample is given by
2.4, 4.6, 3.3, 3.1, 4.6, 2.2, 3.8
is a pivotal quantity, Explain and if yes construct a

Expert Solution

Step 1

The probability density function (PDF) of X is specified as follows:

$\begin{array}{rcl} f_{X} (x; β) & = & \{\begin{cases} \frac{1}{β^{2}} x e^{- \frac{x}{β}}, & x > 0 \\ 0, & e l s e w h e r e \end{cases} \\ = & \{\begin{cases} \frac{1}{Γ (2) β^{2}} {(x)}^{2 - 1} e^{- \frac{x}{β}}, & x > 0 \\ 0, & e l s e w h e r e \end{cases} \end{array}$