3)Which of the following statement is correct:a. If X, Y are independent random variables, then X,Y must be uncorrelated.b. If X, Y are uncorrelated random variables, then X, Y must be independent.c. Both options (a), (b) are correct.d. None

Let, If X and Y are independent then, E(XY) = E(X)•E(Y) and the correlation coefficient between X…

Answered: Which of the following statement is…

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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A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.
If a variable can take certain integer values between two given points, then it is called O a. Continuous random variable O b. Probabilistic random variable c. O c. Deterministic random variable O d. Uncertain random variable O e. Discrete random variable
. An electronic assembly consists of two subsystems A and B. The following probabilities are known. P(A fails) = 0.25, P( A and B fail) = 0.14 and P(B fails alone) = 0.15. Evaluate P (A fails alone) P (A fails given that B has failed) (Explain the solution using Venn diagram)
QL: If Ali drive 4 sessions, he have a 60% chance of winning. Assuming that the sessions are independent of each other, what is the probability that: 1. Ali will win 0, 1,2.3 orall 4 sessions, 2. Ali will win at least one session. 3. Al will win a majority of the sessions.
3b)
Choose the letter that corresponds to the correct answer Which of the following is an example of dicrete variables? a. Weight of students b. Number of purple marble in the basket I. с. Distance travelled between tricycles d. Height of the students in a certain class I. Which are the possible values of the random variable for the number of heads when you toss two coins а. 0,1,2,3 b. 1,2,3 с. 0,1 d. 0,1,2 II. Which of the following statement describe a discrete random variable? a. The average increase in height of baby each year b. The number of avocado produced by an avocado tree each year c. The length of span of a 10 months baby d. The average increase in weight of baby each year Which of the following will yield a higher interest? a. Investing in a bank that offers a simple interest rate of 10% annually for 2 years b. Investing in a cooperative that offers an interest rate of 10% compounding annually for IV. 2 years c. Both A and B d. Saving money in a piggy bank for 2 years Which of…
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. Assume that the box contains balls numbered from 1 through 28, and that 3 are selected. A random variable X is defined as 3 times the number of odd balls selected, plus 4 times the number of even. How many different values are possible for the random variable X?
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A fair dice is thrown once. The random variable Y is related to the number B thrown on the dice as follows. If B is even, then Y is half B, otherwise Y is triple B. Find the mode and E(Y). Select one: no mode and E(Y) = - mode = 3 and E(Y) = 4 mode = 2 and E(Y) = mode = 3 and E(Y) = mode = 5 and E(Y) =

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Which of the following statement is correct: a. If X, Y are independent random variables, then X, Y must be uncorrelated. b. If X,Y are uncorrelated random variables, then X,Y must be independent. c. Both options (a), (b) are correct. d. None с.