2.Suppose that Y is a binomial random variable based on n trials with success probability p andconsider Y* = n - Y.a Argue that for y* = 0, 1, ..., nP(Y* = y*) = P(n − Y = y*) = P(Y = n − y*).b Use the result from part (a) to show thatnP(Y* = y*) = · ( ₁₁² y.)pª²-xq" = ("₁. )¶" p²-x.- y*c The result in part (b) implies that Y* has a binomial distribution based on n trials and"success" probability p* = q = 1 – p. Why is this result "obvious"?

a) To show that for , we can use the properties of the binomial distribution.Y is a binomial random…

Answered: 2. Suppose that Y is a binomial random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose a random variable, x, arises from a binomial experiment with p = 0.26, n = 15. Find P(x ≤ 3): (Give answer as a decimal correct to four decimal places.)Find P(x ≥ 9): (Give answer as a decimal correct to four decimal places.)Find P(x = 7): (Give answer as a decimal correct to four decimal places.)
Suppose that W is a (a = 3, 3 = })-gamma random variable and N is a µ = -Poisson random variable independent of W. What is E (w*]? un for u-Poisson random variable N. n! Note: PN (n) = P (N = n) = e Hint: pmf for a (r, p)-negative binomial random variable is given by n - n = r,r + 1,... r - 1
12
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An analysis of personal loans at a local bank revealed the following facts: 10% of all personal loans are in default (D), 90% of all personal loans are not in default (D'), 20% of those in default are homeowners (HID), and 70% of those not in default are homeowners (H | D'). If a personal loan is selected at random P (H _n D') = _____. 0.63 0.78 O 0.20 0.18 0.90
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2. Let x be a binomial random variable with n=20 and p=.3. Which of the following gives p(x = 13)? • (a) Use binomial table for n=20, p=0.3, and k = 13 • (b) Use binomial table for n=20, p=0.3, and k = 12 • (c) Subtract (b) from (a), i.e. p(x= 13) = p(x ≤ 13) – p(x ≤ 12) PLEASE SHOW ME HOW TO DO IT SO I CAN LEARN IT?
Suppose there is a random Uniform(-1, 1) random variable (Null hypothesis), or Uniform(0,1) (alternative hypothesis) depend on 3 independent sample X1, X2, X3. What is the smallest possible false negative error among all tests with false positive error 1/8?
6. A transportation department is considering placing stop lights at a busy 4-way-stop intersection. Let X1, X2, X3, X4 represent the number of drivers arriving per minute at the respective stop signs. Assume- these to be four mutually independent Poisson random variables with respective means of 2, 5, 4 and 2. (a) Find the mean and standard deviation of S = Xị. (b) Confirm that S ~ Poisson(13) (c) Compute P(S = 0).
Suppose that Y Binomial(n, p) (that is, discrete random variable Y has a Binomial distribution with parameters n and p, where n is a (strictly) positive integer, and 0 < p< 1).
1. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 39
24. Gaussian random variables X, and X,, for which, X, = 2, o = 9, X, =-1, ox, = 4 and Cxx, =-3, are transformed to new random variables Y, and Y, according to जापर डेरें| Y, =-X, + X, Y, =-2X,- 3X, (iii) Cy,Cy, .. Find

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