- 2 The Number Of Defects In A 400 Metre Roll Of Magnetic Recording Tape Has A Poisson Distribution With Unknown Paramete 1 (94.43 KiB) Viewed 72 times
2. The number of defects in a 400-metre roll of magnetic recording tape has a Poisson distribution with unknown parameter μ, which has a prior Gama distribution of the form μ-Ga(3,1). When five rolls of this tape are selected at random and inspected, the numbers of defects found on the rolls are 2, 2, 6, 0 and 3. x9-1 [probability density function of gamma is Ga(x, a, ß) = 0,ß > 0] Γ(α) -Ba e-Bx, x>0₁α > a) Determine expressions for the likelihood function and posterior probability density function of μ. (17 marks) b) Show that the posterior probability mass function of X given the data above is 616r(x + 16) P(μ\X) = 15! x! 7x+16 [Hints: P(u\X) = f(x,μ)ƒ (μ|X)dµ‚μ> 0 and [(x) = f tx-¹e-t dt] (10 marks) c) Given that the median of Beta distribution is m(a, ß) = a+ß- Find the Bayesian estimate of μ under the absolute error loss function. (3 marks)