Give any example of a probability distributionover x and y for a classification problem on the real line, so that the Bayesoptimal classifier isf(x) =1, if x E[1, 3] U[6, 7]-1, otherwise

Bayes Theorem If A1,A2,A3,...An are disjoint sets whose union is the sample space 'S' and E is the…

Answered: Give any example of a probability…

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...

See similar textbooks

Similar questions

Q.3. If the sample space is C = {x : 0 < x < ∞} and C CC where %3D C = {x : 8
2. Suppose X is a discrete random variable with pmf f (x) as shown in the table: X 4 1 2 3 16 4 12 18 f(x) 50 50 50 50 Find the cumulative distribution for X and give a graph of the cdf.
1. What is the expectation of the function g(x1, x2) = x, using the following joint PMF? X1 3 6 2 35% 15% 4 20% 30%
Let (N1,N2,...,Nm) be distributed as Multinomial(n,p1,p2,...,pm). (a). the conditional covariance between Ni and Nj for i, j ≤ r given (N(r+1), . . . , Nm) (b). an appropriate approximation to the probability that N1 is larger than 65 when N = 100 and p1 = 0.25
The random variable Z is defined as a function of the random variables X and Y as follows: Z = 1 Moreover, it is known that E[X|Z] = Z² and that Z is zero mean. Compute E[Y|Z = 2] Y+1 and E[Y].
You are given a two dice with 4 sides each, with equal probability of landong on all sides. Dice one has values 1 - 4 and the second has values 5-8. The low-valued die (dice one) is rolled first. If you get a 1 or 2, then you roll the high-valued die (dice 2). If you get 3 or 4, you roll the low-valued die. X= value of the 1st roll Y = value of the 2nd roll Z = X + Y %3D Find H(X), H(Y), H(Z) Find H(Y|X) Find H(X,Y), H(XIҮ) Find I (X;Y)
A lot of 25 light bulbs consists of N₁ defectives and N₂ working bulbs. The buyer accepts the lot of N₁ + N₂ = 25 bulbs if the number of defectives, X among n = 5 items taken at random and without replacement from the lot is less than or equal to 1. The operating characteristic curve is defined as the probability of accepting the lot, namely OC (p) = P(X ≤ 1) = P(X = 0) + P(X = 1), where p = N₁/25 is the probability of a bulb being defective. (a) Show that the probability of the picking exactly X defectives follows a hypergeometric distribution. (b) Determine the operating characteristic curve for p = 0.04, p = 0.08, p = 0.12 and p = 0.16. (c) Plot, using R, the operating characteristic curve for N₁ = 1 to N₁ = 4.
An individual has a vNM utility function over money of u(x) = Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra $9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9. What probability, p, of losing $7 would make the individual indifferent between to play and to not play the lottery? (Make sure to answer in the form, 0.X, i.e. 0.25) Enter your answer here
Suppose X has a trivariate normal distribution with mean vector 0 and covariance matrix 1 0.5 0.25 0.5 1 0 0.25 0 1 A. Find the joint distribution of W1 = X1+X2+X3 and W2 = X1 - X3 B. Find the joint distribution of (X1, X2) GIVEN X3=X3 C. P(max(X1,X2)<X3) D. P(X1>X2|X3=1)
2. Find E(X) and Var(X) if a. P(X = 0) = 0.2, P(X = 1) = 0.3, and P(X = 2) = 0.5. b. X is the number of successes in 200 Bernoulli trials each with probability of success 0.7.
A1

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Give any example of a probability distribution over x and y for a classification problem on the real line, so that the Bayes optimal classifier is f(x) = 1, if x E[1, 3] U[6, 7] -1, otherwise