(a) (b) Suppose that the random variables X,..., X, form a random sample from a standard...

  

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(a) (b) Suppose that the random variables X₁,..., X, form a random sample from a standard normal distribution. Let Y = (X₁ + X₂ + X₂ + X₂)² + (X₂ + X6 + X₁ + Xg)². 7 Obtain the c value so that the random variable cY has a x² distribution. [10 marks] Suppose that X₁,..., X, are independent and identically distributed random variables from a standard normal distribution. Obtain the value of d so that the random variable has at distribution. d(X₁ + X₂ + X3) 2 2 2 (X² + X² + X² + X₂²)¹/² 4 7 [10 marks] (c) If S and S are the variance for the sample of independent random variables with size n₁ =6 and n₂ =10, taken from a Normal distribution with common variance, calculate the value of e so that P(S²/S² <e) = 0.05. [10 marks] (a) (b) Suppose that the random variables X₁,..., X, form a random sample from a standard normal distribution. Let Y = (X₁ + X₂ + X₂ + X₂)² + (X₂ + X6 + X₁ + Xg)². 7 Obtain the c value so that the random variable cY has a x² distribution. [10 marks] Suppose that X₁,..., X, are independent and identically distributed random variables from a standard normal distribution. Obtain the value of d so that the random variable has at distribution. d(X₁ + X₂ + X3) 2 2 2 (X² + X² + X² + X₂²)¹/² 4 7 [10 marks] (c) If S and S are the variance for the sample of independent random variables with size n₁ =6 and n₂ =10, taken from a Normal distribution with common variance, calculate the value of e so that P(S²/S² <e) = 0.05. [10 marks]

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Answer and Explanation 1 It is stated that X1 X2 X6 N0 1 and Y X X2 X3 X4 X5 X6 Wev... View the full answer