Example 16-22. If F(n1, n2) represents an F-variate with n¡ and n2 d.f., prove that F(n2, n1) is distributed as 1/F(n, n2) variate. Deduce that P[F(n1, n2) 2 c] = P| F(n2, n1) < %3D

A random variable x follows continuous uniform distribution on the interval [18,38]. Find the variance V ar (X). Answer should be with 2 decimal places.

The edge roughness of slit paper products increases as knife blades wear. Only 1% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 5% of products slit with worn blades exhibit roughness. If 25% of the blades in manufacturing are new , 60% are of average sharpness, and 15% are worn , what is the proportion of products that exhibit edge roughness? Let R = edge roughness N = new blades A = blades with average sharpness W = worn blades What are the mathematical notation for the following values: 1% = 3% = 5% = 25% = 60%= 15% = Express the question in mathematical notation; The proportion of products that exhibit edge roughness* = *Express in rational number with 2 decimal places.