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QUESTIONX1Xz X16independent random varlables each having slandard normal distribution and Yi, Yz -'Ys having Chi-square distrbution with degrees of freedom:...

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QUESTIONX1Xz X16independent random varlables each having slandard normal distribution and Yi, Yz -'Ys having Chi-square distrbution with degrees of freedom: State the distnbution and parameter(s) of the following variables:a) U =2x1 ' Xa + Xs + Xz]-3Xz(3 marks)b) K = 5 where U is defined in (a)marks c) V =xZ-X?+Ys -K2_(3 marks}s-Xy(2 marks)Jsk 0} W =(2 marks)CU2 0 Let Q = follaws F-distribution with parameters the value constant write the degrees of freedom for Qrespectively- Detemi

QUESTION X1Xz X16 independent random varlables each having slandard normal distribution and Yi, Yz -'Ys having Chi-square distrbution with degrees of freedom: State the distnbution and parameter(s) of the following variables: a) U =2x1 ' Xa + Xs + Xz]-3Xz (3 marks) b) K = 5 where U is defined in (a) marks c) V =xZ-X?+Ys -K2_ (3 marks} s-Xy (2 marks) Jsk 0} W = (2 marks) CU2 0 Let Q = follaws F-distribution with parameters the value constant write the degrees of freedom for Q respectively- Detemine marks}



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Given a standard normal distribution, find the area under the curve that lies (a) to the left of $z=-1.10$; (b) to the right of $z=1.645$; (c) between $z=-2.43$ and -0.45 ; (d) to the left of $z=0.45$; (e) to the right of $z=-0.45$; (f) between $z=-0.45$ and $z=0.45$.


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