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)

for the points

step-by-step explanation:

step-by-step :

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

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