2 years ago

Please help giving brainliest:)

Mathematics

1 answer:

Galina-37 [17]2 years ago

8 0

Answer:

10*(9-5)

Step-by-step explanation:

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Suppose u1, u2, ..., un are independent random variables and for every i = 1, ..., n, ui has a uniform distribution over [0, 1].

sattari [20]

$Z=U_{(1)}=\min\{U_1,\ldots,U_n\}$

has CDF

$F_Z(z)=1-(1-F_{U_i}(z))^n$

where $F_{U_i}(u_i)$ is the CDF of $U_i$ . Since $U_i$ are iid. with the standard uniform distribution, we have

$F_{U_i}(u_i)=\begin{cases}0&\text{for }u_i$

and so

$F_Z(z)=1-(1-F_{U_i}(z))^n=\begin{cases}0&\text{for }z$

Differentiate the CDF with respect to $z$ to obtain the PDF:

$f_Z(z)=\dfrac{\mathrm dF_Z(z)}{\mathrm dz}=\begin{cases}n(1-z)^{n-1}&\text{for }0$

i.e. $Z$ has a Beta distribution $\beta(1,n)$ .

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2 years ago

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Step-by-step explanation:

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Diano4ka-milaya [45]

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Step-by-step explanation:

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