1, Suppose that a ramdom variable X has an F distribution with 3and 8 degrees of

Question

1, Suppose that a ramdom variable X has an F distribution with 3and 8 degrees of freedom . Determine the value of c such thatP(X<c)=0.05

2, Suppose that a random variable X has an F distribution with 1and 8 degrees of freedom. Use the table of the t distributionto determine the value of c such that P(X>c)=0.2

3, Suppose that X1,...,X6 form a random sample from a standardnormal distribution and let
Y=(X1+X2+X3)^2+(X4+X5+X6)^2
determine a value of c such that the random variable cY will haveX^2 distribution

Explanation / Answer

1. P(X<c)=0.05
Consider the tables of F-distribution at 0.05 we have the value ofc = 4.07, with v1 = 3and v2 = 8 degrees of freedom 2. P(X>c)=0.2 implies 1-P[X<c] = 0.2 implies P[X<c] = 0.8 Consider the tables of F-distribution at 0.05 we have thevalue of c = 0.07, with v1 = 1 andv2 = 8 degrees of freedom

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