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Problem 4 (4 points) Let Y be the number of children per family with the following...
Question 4: Let X and Y be two discrete random variables with the following joint probability...
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
Let the random variable x represent the number of girls in a family with three children....
Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.31. The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls? 0 1 2 3 P(x) 0.329 0.443 0.199...
For families with 4 children, let XX be the number of children with Genetic Condition B....
For families with 4 children, let XX be the number of children with Genetic Condition B. Can the following table be a probability distribution for the random variable XX? xx P(x)P(x) 0 0.2213 1 0.1585 2 0.177 3 0.1985 4 0.2447 yes no
8. Let the random variable x represent the number of girls in a family with three...
8. Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.35 The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls? x P(x) 0 0.275 1 0.444 2 ...
Please solve the below question with explanation Let X be the number of children in an...
Please solve the below question with explanation Let X be the number of children in an ordinary American family. Let P(X=i)=Pi, for i=1,2,3,4, and P(X>4)=0, what is the probability that there are at least two girls in a family? Assuming the gender of each baby is identical independent distributed, with probability being a girl q. Let Y be the number of girls in a family.
In government data, a household consists of all occupants of a dwelling unit, while a family...
In government data, a household consists of all occupants of a dwelling unit, while a family consists of two or more persons who live together and are related by blood or marriage. So all families from households, but some households are not families. Here are the distribution of household size and of family size in the United States: Number of persons 3 4 5 6 7 Household probability 0.30 0.16 0.03 0.14 0.37 Family probability 0.44 0 0.22 0.09 0.25...
Applied and Computational Questions 1. Pairs of random numbers (r, y) a. How many different pairs...
Applied and Computational Questions 1. Pairs of random numbers (r, y) a. How many different pairs are possible? are generated. X and Y are integers between 0 and 5 inclusive. a random variable W is defined to equal the absolute value of the difference between X b. Suppose and Y. How many distinct values are possible for W? Give the pair of dice is rolled once. 2. Let x represent the number of times a one appears when a probability...
It is known that time spent partying per month by Kent State students is normal with...
It is known that time spent partying per month by Kent State students is normal with a mean of 46 hrs and standard deviation of 4 hrs. What is the probability that a randomly chosen Kent State student spends more than 49 hours partying per month? 1. 0 2. 0.0668 3. 0.8535 What is the probability that a randomly selected Kent State student spends less that 40 hours partying per month? 4. 0.2266 For which one of the following sets...
Let x determine a random variable, and use your knowledge of probability to prepare a probability distribution A family has three children and the number of girls is recorded. (Assume an equal ch...
Let x determine a random variable, and use your knowledge of probability to prepare a probability distribution A family has three children and the number of girls is recorded. (Assume an equal chance of a boy or girl for each birth) Complete the probability distribution. P(x) (Type an integer or a simplified fraction )
Let x determine a random variable, and use your knowledge of probability to prepare a probability distribution A family has three children and the number of...
2. Suppose that a family is going to keep having children until they have at least...
2. Suppose that a family is going to keep having children until they have at least one girl. Further suppose we can model successive births as boy and one independent trials with p P(girl) and P(boy) = 1 - p. Let Y denote the total number of children in the family. Compute, for y 2, (i) the probability that the first boy born is the y-th child born; [2] (ii the probability that the first girl born is the y-th...
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.31. The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls? 0 1 2 3 P(x) 0.329 0.443 0.199...
Applied and Computational Questions 1. Pairs of random numbers (r, y) a. How many different pairs are possible? are generated. X and Y are integers between 0 and 5 inclusive. a random variable W is defined to equal the absolute value of the difference between X b. Suppose and Y. How many distinct values are possible for W? Give the pair of dice is rolled once. 2. Let x represent the number of times a one appears when a probability...
It is known that time spent partying per month by Kent State students is normal with a mean of 46 hrs and standard deviation of 4 hrs. What is the probability that a randomly chosen Kent State student spends more than 49 hours partying per month? 1. 0 2. 0.0668 3. 0.8535 What is the probability that a randomly selected Kent State student spends less that 40 hours partying per month? 4. 0.2266 For which one of the following sets...
Let x determine a random variable, and use your knowledge of probability to prepare a probability distribution A family has three children and the number of girls is recorded. (Assume an equal chance of a boy or girl for each birth) Complete the probability distribution. P(x) (Type an integer or a simplified fraction )
Let x determine a random variable, and use your knowledge of probability to prepare a probability distribution A family has three children and the number of...
2. Suppose that a family is going to keep having children until they have at least one girl. Further suppose we can model successive births as boy and one independent trials with p P(girl) and P(boy) = 1 - p. Let Y denote the total number of children in the family. Compute, for y 2, (i) the probability that the first boy born is the y-th child born; [2] (ii the probability that the first girl born is the y-th...
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