- #1
mathmajor23
- 29
- 0
Homework Statement
Let Xi ~ iid f(x) = (2x)I[0,1](x), i = 1,...,n.
Find the distribution of X(1). What is the probability that the smallest one exceeds .2?
mathmajor23 said:Homework Statement
Let Xi ~ iid f(x) = (2x)I[0,1](x), i = 1,...,n.
Find the distribution of X(1). What is the probability that the smallest one exceeds .2?
mathmajor23 said:FX(1)(x) = P(X(1) <= x)
= P(X1,...,Xn <= X)
=1-P(X1,...,Xn > X)
=1-P(X1>X)^n since the xi's are iid.
=1-[1-P(X1 <= X)]^n
=1-[1-F(x)]^n
=1-[1-∫ from 0 to x (2tdt)]^n
=1-(1-X^2)^n
For the probability, P(X1>.2) = 1-Fx(1) (0.2) = (1-(0.2)^2)^n = (0.96)^n
Order statistics probabilities refer to the probabilities associated with the arrangement of a set of numbers in ascending or descending order. It is commonly used in statistics to analyze the distribution of a set of data.
The order statistics probabilities can be calculated using the formula P(X≤x) = F(x)^n, where P(X≤x) is the probability of x or less numbers, F(x) is the cumulative distribution function, and n is the number of terms in the set.
Order statistics probabilities help in determining the relative position of a data point within a set of data and provide insights into the distribution of the data. It is also used in hypothesis testing and estimating various statistical parameters.
No, order statistics probabilities can only be used for numerical data. It is not applicable to non-numerical data such as categories or labels.
Order statistics probabilities can be applied in various fields such as finance, economics, and engineering to analyze and interpret data. It can also be used for decision making, forecasting, and risk analysis.