Q3: Let X₁, X2, ......., Xn be i.i.d from Gamma distribution (x~ GAM( e, 3), show that s= sufficient for e (HINT Σx, ~ GAM (0, 3n))
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- Suppose X = 1/(1+Y), where 3 Y ~ fy(y) = 12 1+y y > 0, 0, otherwise. Identify the distribution of X by name and parameter values.Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distributiont x, x, ... x be a random sample from an exponential distribution with parameter 0. Find sufficient estimator for '8'.
- Let X~N(0, 0'). Find the CRLB for variances of the unbiased estimator of T(0)= 0?.X is a normally normally distributed variable with mean μ = 30 and standard deviation σ = 4. Finda) P(x < 40)b) P(x > 21)c) P(30 < x < 35)X1,..., X, are independent, identically distributed RVs with mean u and variance g?. Find the mean of S- Σ(Χ,-X), where X= -ΣΧ,
- 2.2 Explain how to generate from the Beta (1, 3) distribution using the inverse- transform method.Let X1,…,Xn be i.i.d. Exp(λ) random variables, where λ is unknown. What is the distribution of min1≤i≤n(Xi)? Enter the pdf fmin(x) of mini(Xi) in terms of x. fmin(x) and give an unbiased estimator θ^ for 1/λ.2) Let X be a continuous random variable with PDF 0SEE MORE QUESTIONS