Answered: Let X - Poisson(1). Show that if x is a… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 64E

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Question

Let X - Poisson(1).
Show that if x is a positive integer, then
a.
P(X = x)
P(X = x- 1) x
Show that if X - Poisson(1), the most probable value for X is the greatest integer less
than or equal to 2. [Hint: Use part (a) to show that P(X = x) > P(X = x – 1) if and only
b.
if x < A.]

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31. Prove statement of Theorem : for all integers and .
Let f(x),g(x),h(x)F[x] where f(x) and g(x) are relatively prime. If h(x)f(x), prove that h(x) and g(x) are relatively prime.
Prove the conjecture made in the preceding exercise.
If n is 30 and p is 0.04. using the Poisson approximation to the Binomial, the P(X < 2) is equal to a 0.4101 b. 0 .2103 C 0.0867 d. 0 .8795
3.) Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)? What is P(X = 0)?
Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x. n = 4, x = 1. n = 2, x = 2 n = 2, x = 0.
Let X1, . . . , Xn, . . . ∼ iid Bern(θ). Consider the Bayes estimator under squared error loss with the Unif(0,1) prior. Show that this estimator is consistent.
A certain market has both an express checkout line and a superexpress checkout line. Let X1 denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X1 and X2 is as given in the accompanying table. x2 0 1 2 3 x1 0 0.09 0.07 0.04 0.00 1 0.05 0.15 0.05 0.04 2 0.05 0.03 0.10 0.06 3 0.01 0.02 0.04 0.07 4 0.00 0.02 0.05 0.06 (a) What is P(X1 = 1, X2 = 1), that is, the probability that there is exactly one customer in each line?P(X1 = 1, X2 = 1) = (b) What is P(X1 = X2), that is, the probability that the numbers of customers in the two lines are identical?P(X1 = X2) = (c) Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X1 and X2. A = {X1 ≥ 2…
We now need to attempt to find an exact value for n such that P(r ≥ 1) = 0.99. Clearly, if the bank has any chance of detecting a burglar they will need to have at least one alarm installed. So, we know that, minimally, n must be at least 1.Since n must be at least 1, suppose we start by trying n = 2, where there will be two alarms. When there are two alarms, r ≥ 1 means either one or both alarms could detect the burglar. If neither alarm detects the burglar it is considered a failure. Therefore, P(r ≥ 1) can be calculated using either of the following formulas. P(r ≥ 1) = P(1) + P(2) P(r ≥ 1) = 1 − P ( ___ ) fill in the blank
A manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Determine the following. 1) fxy(x,y) 2) fx (x)3) fY|2 4) E(x)Show all work
A manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Determine the following. 1) fxy(x,y) 2) fx (x)3) E(x)4) E(Y|X=2)5) V(Y|X=2)6) Are X and Y independent? Why?

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