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- For a binomial distribution with parameters n=25 and p=0.70, determine the continuity correction for normal approximation for: a) P( X = 20) b) P( X > 20) c) P(X ≤ 20) d) P(X≥ 20)Could you solve (g),(h)? Thank you.Assume that X is a random variable whose conditional distribution given the variable Y is poisson P (X | Y) = Po (Y). Suppose further that Y has a gamma distribution Y ∼ Gamma (1, 1). (a) Determine the value E (XY). (b) Determine the conditional distribution P (Y | X).
- Let X1, X2, .., Xn be a sample from a Continuous Unif(u - Ō, µ + d) distribution. Please find the moment estimators (MoM) for µ and ō. [Note] ð > 0. .... (b-a)? [Hint]: If X - Unif (a, b), then E(X)="", V(X)="1" a+lSuppose that a random sample of sizen is taken from a Poisson distribution for which the value of the mean e is unknown, and the prior distribution of e is a gamma distribution for which the mean is Po. Show that the mean of the posterior distribution of e will be a weighted average having the form Y,X, + (1– Yn)Ho, and show that yn →1 as n- *.Let X; € {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2,..., Xn fxp(x | p) = (1 – p)*-'p for 0 < p < 1 defined on x E {1,2, 3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 1. Using a p~ Beta(a, B) prior, derive the posterior density of p, fp|X, (p | Xn).
- 23. Through a point B on the y-axis whose ordinate is possible and equal to a, a straight line is drawn in a direction taken at random in the < 0 < 4 4 O being the inclination of the line to B0. Examine the inteval - probability distribution of the intercept x on the x-axis.6. The amount of a loss X follows the uniform distribution on [0, 100]. An insurance policy on this loss has an ordinary deductible of 10, a maximum amount paid of 50, and a coinsurance of 80%, which is applied after the deductible. After losses are subject to inflation of 10%, calculate the expected claim amount paid per loss on this policy.c) Suppose that a random variable Y is uniformly distributed on an interval (0,1) and let c> 0 be a constant. i) Find the moment generating function of X = -cY. ii) What is the distribution of X? 2| Page