(a) Assume the sample variances to be continuous measurements. Find the proba- bility that a random sample of 25 observations, from a normal population with variance o² = 6, will have a sample variance S² (with resolution 0.01) i. Greater than 9.1 ii. Between 3.462 and 10.745

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(a) Assume the sample variances to be continuous measurements. Find the proba-
bility that a random sample of 25 observations, from a normal population with
variance o² = 6, will have a sample variance S² (with resolution 0.01)
i. Greater than 9.1
ii. Between 3.462 and 10.745
(b) Given X₁, X₂ ~ Exp(1), Y
Exp(2), also X₁, X2, Y are all independent, what
distribution does the RV Z = X+X follow? (Your result should be things like "it
AY
follows a normal distribution with parameters μ = 0 and o² = 1.")
(Hint: HW8 Q6(a) may help.)
Transcribed Image Text:(a) Assume the sample variances to be continuous measurements. Find the proba- bility that a random sample of 25 observations, from a normal population with variance o² = 6, will have a sample variance S² (with resolution 0.01) i. Greater than 9.1 ii. Between 3.462 and 10.745 (b) Given X₁, X₂ ~ Exp(1), Y Exp(2), also X₁, X2, Y are all independent, what distribution does the RV Z = X+X follow? (Your result should be things like "it AY follows a normal distribution with parameters μ = 0 and o² = 1.") (Hint: HW8 Q6(a) may help.)
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