I,Λ2, X3 , X4,X5 be a sample from N

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

Here,

~ Normal(0, 1), 2-1, 2, 3, 4, 5

That implies,

$sum_{i=1}^{5}rac{X_i^2 }{4} sim chi^2_{1}, i = 1,2,3,4,5$

and by additive property of chi square distribution,

$sum_{i=1}^{5}rac{X_i^2 }{4} sim chi^2_{5}$

To find

5 Pl 〉 X > 5,75)

5 = 1-P(〉 X < 5.75)

$= 1 - P(sum_{i=1}^{5}rac{X_i^2}{4} leq rac{5.75}{4})$

$= 1 - P(chi^2_{5} leq 1.43750)$

= 1 - 0.0798324

= 0.920168

Answer 2

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