Question

求帮我解一道高数概率密度题 设随机变量X的概率密度为：f(x)=A/根号（1-x²）,|x|

Answer 1

(1)∫[-1,1]f(x)dx

=∫[-1,1]A/√(1-x^2)dx

=A*[arcsinx]|[-1,1]

=A*[π/2-(-π/2)]

=πA

=1

A=1/π

(2)P{-1/2≤X≤1/2}

=∫[-1/2,1/2]f(x)dx

=1/π*[arcsinx]|[-1/2,1/2]

=1/π*[π/6-(-π/6)]

=1/π*π/3

=1/3

(3)F(x)=∫f(x)dx

=∫1/π*/√(1-x^2)dx

=1/π*arcsinx+C