Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of boys in each outcome. For example, if the outcome is gbg, then R(gbg) = 1. Suppose that the random variable X is defined in terms of R as follows: \( X = 2R^2 - 2R - 4 \). The values of X are given in the table below.| Outcome | gbb | bgg | bbg | ggb | bgb | gbg | ggg ||---------|-----|-----|-----|-----|-----|-----|-----|| Value of \( X \) | 0 | -4 | 0 | -4 | 8 | 0 | -4 | -4 |Calculate the values of the probability distribution function of X, i.e., the function \( p_X \). First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.Below the text, there's a diagram divided into blocks where the value \( x \) of \( X \) is displayed as a question mark placeholder, and a row below awaiting the insertion of the probabilities \( p_X(x) \). The specific probability boxes are unfilled, allowing for completion.

Answered: Image /qna-images/answer/5c2adf57-c231-40b5-bb8d-01174867086d.jpg

Answered: Suppose that the genders of the three…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A psychologist found a study which claiming that 32% of patients who visit a psychologist have symptoms of anxiety. This psychologist had 44 patients visit. Let x = the number of patients that had symptoms of anxiety. (a) The random variable is which of the following? O the number of psychologists O the number of patients who visited the psychologist the number of patients who had symptoms of anxiety O the number of patients without symptoms of anxiety (b) How many total patients did the psychologist have visit?
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.
In experiment of flipping two coins, each coin has two faces: Head and Tail. Each face is being equally likely to be drawn. If two random variables X and Y are defined as X(s) = Number of Heads appeared on both coins Y(s) = Number of Tails appeared on both coins The value of pxy (2,0) is 00.5 00 01 00.25
A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 25% of the people get vaccinated. If a person is selected at random, what is the probability that he or she will contract the disease?
The genotype of an organism can be either normal (wild type, W) or mutant (M). Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring.
If you have a sample of 100 patients at a hospital and 20 of them have the flu, what is the probability Of randomly selecting 3 patients in a row who have the flue?
I will be glad if the answer comes quickly
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is tth, then =Rtth1. Suppose that the random variable X is defined in terms of R as follows: =X−R2−3R4. The values of X are given in the table below. Outcome htt tht hth thh ttt hhh hht tth Value of X −6 −6 −6 −6 −4 −4 −6 −6 Calculate the values of the probability distribution function of X, i.e. the function p X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.
If 3 % of the electric bulbs manufactures by a company are defective, find the probability that in a sample of 100 bulbs: a. 0 bulbs will be defective b. 1 bulbs will be defective c. 2 bulbs will be defective d. 3 bulbs will be defective e. 5 bulbs will be defective
A large bag contains pretzels with 3 different shapes: heart, square, circle . Billy plans to reach into the bag and draw out one pretzel at a time, stopping only when he has at least one pretzel of each type. Let the random variable X denote the number of pretzels that Billy will draw from the bag. You can assume that there is an infinite number of pretzels in the bag with equal proportions of each shape. Find E(X).
In a class there are 18 juniors and 10 seniors; 6 of the seniors are females, and 12 of the juniors are males. If a student is selected at random, find the probability of selecting the following A junior or a female A junior or a senior A junior who is a female

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