We denote this distribution Exp(\). (i) For 0 < p < 1, compute the 100p-th percentile of Exp(\), i.e. compute the quantile function Q(p). (ii) What is the median of Exp(\)?
We denote this distribution Exp(\). (i) For 0 < p < 1, compute the 100p-th percentile of Exp(\), i.e. compute the quantile function Q(p). (ii) What is the median of Exp(\)?
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![A random variable X has an exponential distribution with parameter λ if its CDF equals
e-xt,
Fx(t) =
1
0,
=
t> 0
t≤0
We denote this distribution Exp(\).
(i) For 0 < p < 1, compute the 100p-th percentile of Exp(\), i.e. compute the quantile
function (p).
(ii) What is the median of Exp(\)?
·
9
2
(iii) Suppose X₁, X2, Xn are independent exponential RV's with parameters A₁, A2,
min(X₁, X₂, ..., Xn). Compute the CDF of Y and use this to show that Y
Let Y
also has an exponential distribution.
An.
···,
(iv) In the setting of previous part, let Z = max(X₁, X2, Xn). Compute the CDF of
Z. Does Z have an exponential distribution?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33efa0ee-e3c4-4640-bf2a-d63d72536f00%2F0e959ecf-3e45-4a32-b4bc-56741773c14b%2F2ufs7b_processed.png&w=3840&q=75)
Transcribed Image Text:A random variable X has an exponential distribution with parameter λ if its CDF equals
e-xt,
Fx(t) =
1
0,
=
t> 0
t≤0
We denote this distribution Exp(\).
(i) For 0 < p < 1, compute the 100p-th percentile of Exp(\), i.e. compute the quantile
function (p).
(ii) What is the median of Exp(\)?
·
9
2
(iii) Suppose X₁, X2, Xn are independent exponential RV's with parameters A₁, A2,
min(X₁, X₂, ..., Xn). Compute the CDF of Y and use this to show that Y
Let Y
also has an exponential distribution.
An.
···,
(iv) In the setting of previous part, let Z = max(X₁, X2, Xn). Compute the CDF of
Z. Does Z have an exponential distribution?
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