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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Q10. The probability model for a random variable A is [% ,a=-1 P₁(a)=% a=1 0, otherwise The conditional probability model for random variable B is: %,b=0 P (b/-1)=% .b=1 0, otherwise P (b/1)=,b=1 0, otherwise a) What is the probability model for random variables A and B If 4-1, what is the conditional expected value E[BA-11? c) If B-1, what is the conditional PMF Pa (at)? b) d) If B-1, what is the conditional variance Var [4| B=1]? 110 marke
If x is functionally related to A and B as x = A + B, and if A and B are random variables, then x is also a random variable. True or False
If a dicrete random variable x takes only three values 2,5 and 9 and that p(x=2)= 0.2 , p(x=5) = 0.5, then what is the value of P (X=9) ?
Scenario 1 A basket contains 3 red and 4 green balls. A random experiment is performed such that a ball is randomly drawn from the basket, replaced back in the basket and then again a ball is randomly drawn from the basket. Let X is a random variable containing the count of red colored balls at the end of two trials. Scenario 2 A basket contains 3 red and 4 green balls. A random experiment is performed such that a ball is randomly drawn from the basket, not replaced back in the basket and then again a ball is randomly drawn from the basket. Let X is a random variable containing the count of green colored balls at the end of two trials. Now answer the following questions. Compare the two scenarios by showing probability tree diagrams of the two. Examine and comment on the shape of the distribution for the two scenarios.
A nurse has found that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 11%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu. Let the random variable ✗ be the number of patients, out of the 25 who called the medical help line, that actually have the flu. How is X distributed? ✗~B 25 0.11 Find the probability that exactly 9 of the 25 patients actually have the flu. Find the probability that fewer than 8 of the 25 patients actually have the flu. Find the mean of the distribution. Find the standard deviation of the distribution. Part 2 of 2
In the western United States, there are many dry land wheat farms that depend on winter snow and spring rain to produce good crops. About 70% of the years there is enough moisture to produce a good wheat crop, depending on the region. Let r be a random variable that represents the number of good wheat crops in n = 8 years. Suppose the Zimmer farm has reason to believe that at least 4 out of 8 years will be good. However, they need at least 6 good years out of 8 years to survive financially. Compute the probability that the Zimmers will get at least 6 good years out of 8, given what they believe is true; that is, compute P(6 ≤ r | 4 ≤ r). (Round your answer to three decimal places.) Let r be a random variable that represents the number of good wheat crops in n = 10 years. Suppose the Montoya farm has reason to believe that at least 6 out of 10 years will be good. However, they need at least 8 good years out of 10 years to survive financially. Compute the probability that the Montoyas…
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 N be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then = Nhht1. Suppose that the random variable X is defined in terms of N as follows: =X−2N2−4N3. The values of X are given in the table below. Outcome ttt hhh htt hht thh tht hth tth Value of X 3 −3 −3 −5 −5 −3 −5 −3 Calculate the probabilities P (X = x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X P (X = x)
In large corporations, an "intimidator" is an employee who tries to stop communication, sometimes sabotages others, and, above all, likes to listen to him or herself talk. Let x1 be a random variable representing productive hours per week lost by peer employees of an intimidator. x1: 7 3 6 2 2 5 2 A "stressor" is an employee with a hot temper that leads to unproductive tantrums in corporate society. Let x2 be a random variable representing productive hours per week lost by peer employees of a stressor. x2: 3 3 10 8 6 2 5 8 x1: 3.8571 s1: 2.1157 | x2: 5.625 s2: 2.8754 | Level of Significance: 0.05 | H0: ?1 = ?2; H1: ?1 < ?2 got the value of the sample test statistic wrong but its unchangeable. I need help finding the 90% confidence interval for ?1 − ?2 (rounded answer to 2 decimals)
4. A newly married couple wants to have children until they obtain children of both sexes. The events of having a boy or girl are independent and equiprobable. Let X be the random variable that counts the number of children that the couple has until obtaining children of both sexes. For example, X (bbbbbbg) = 7 and X(ggggggggb) = 9 where b stands for 'boy' and g stands for 'girl'. (Note that X is not a negative binomial random variable because having a girl or a boy is considered a success. In fact, X is not one of the standard discrete random variables discussed in class.) (a) Write down the pmf of X, and do not forget to indicate the range of values that x can take on. px (x) = (b) What is the probability that the couple will have to have at least five children to obtain children of both sexes? Express your answer as a fraction.
just this multichoice question please
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 N be the random variable counting the number of heads in each outcome. For example, if the outcome is ttt, then N (ttt) = 0. Suppose that the random variable X is defined in terms of N as follows: X = 2N−2N2 - 1. The values of X are given in the table below. Outcome ttt hht tth htt hhh tht hth thh Value of X −1 −5 −1 −1 −13 −1 −5 −5 Calculate the probabilities P (X = x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X P (X = x)
After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. At the beginning of the next lecture, the professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to have left books. One possible outcome is that 1 receives 2's book, 2 receives 4's book, 3 receives his or her own book, and 4 receives 1's book. This outcome can be abbreviated as (2, 4, 3, 1). (a) List the other 23 possible outcomes. (1 2 3 4) (1 2 4 3) (1 3 4 2) (1 3 2 4) (1 4 3 2) (1 4 2 3) (2 1 4 3) (2 1 3 4) (2 3 4 1) (2 314) (2431) (2 × (b) Let X denote the number of students who receive their own book. Determine the pmf of X. (Enter your answers as fractions.) 0 1 2 3 4 X p(x) 0.375 ✓ 0.333 0.25 0 0.041666 X

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