Question

If X is continuous uniform on the interval (0, 10), find P (X+ (10/X) > 7). @Statistics

Answer 1

normally you cannot multiply both sides of an inequality by x, but you can in this case because you know that x is positive.

Answer 2

so you get
\[x+\frac{10}{x}>7\]
\[x^2+10>7x\]
\[x^2-7x+10>\]
\[(x-2)(x-5)>0\] and so
\[x<2,x>5\]

Answer 3

therefore the lengths are from 0 to 2 is 2 and from 5 to 10 is 5 for a total length of 7
divide by the length of the entire interlval to get
\[P(X+\frac{10}{X}>7)=\frac{7}{10}=.7\]

Answer 4

thanks man! can youi help me on my other question, please?