Let X1, X2, ..., X5 be a random sample of size n = 5 from the normal distribution N(0, θ). (a) Argue that the ratio R = (X2 1 + X2 2 )/(X2 1 + ... + X2 5 ) and its denominator (X2 1 + ... + X2 5 ) are independent. (b) Does 5R/2 have an F-distribution with 2 and 5 degrees of freedom? Explain your answer. (c) Compute E(R)

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

so mark-up is 0.4 multiplied by 180 = 72