# family

1. ### Family of Three Children - Conditional Probability

From families with three children, a family is selected at random and found to have a boy. What is the probability that the boy has (a) an older brother and a younger sister; (b) an older brother; (c) a brother and a sister? Assume that in a three-child family all gender distributions have equal...
2. ### integral related a spectral family

Hello, how to define an integral from a spectral family? for Riemann integral, we fix an epsilon, we use upper sums, lower sums, a partition, etc.... then we proof that this integral is independent for the choice of this partition and this epsilon , but here what is the main idea? how is it...
3. ### Family of Finite Sets

Let $\left \{ F_{j} \right \}_{j \in \mathbb{N}}$ a family of nonempty sets such that $F_{j}$ is finite $\forall j \in \mathbb{N}$. Let $g: F_{j+1} \rightarrow F_{j}$ a function that associates $f \in F_{j+1}$ to an element in $F_{j}$. Prove that is always possible to choose an element \$f_{j}...

5. ### Ensuring test assumptions are met in a GLMM or GEE when using non-gaussian families

Hi all, I've been trying to test some of my data using either a GLMM or a GEE in R. When using a gaussian family with an identity link function, I can easily assess that the assumptions of normality and homoscedasticity are met by using a qqplot and Shapiro-Wilks test on the residuals for the...
6. ### A family of functions where each member is its own inverse?

A family of functions is a set of functions that share one or more properties. ie: The family of quadratics with zeros 1 and 10, or the linear functions with a slope of 20. there is a family of linear functions where each member is its own inverse. What linear property defines the family? (I...
7. ### In a family of 5 children, determine the following probabibilities?

Hi, I'm a bit confused with one part of this probability problem. I'm pretty sure I got part a and b, but I'm not sure about c. A family has 5 children, determine the following probabilities a.) All 5 are the same gender b.) 3 are boys, and 2 are girls c.) The 3 oldest are boys, and the 2...
8. ### SOLVED Find the differential Equation of the given Family

I have a series of questions that deal with this but i can't seem to get any correct. Here is the first question. y=Cx2+2 I cant find an example that walks me through this, so any help is appreciated so i can tackle the rest of the questions. Thanks.
9. ### HELP! D.E.of a family of circles tangent to the x-axis :))

Find the Differential Equation of Family of Circles Tangent to the X-axis! Thank you to those who will help :)))
10. ### one-parameter family of solutions

How do I "guess" a one-parameter family of solutions to the differential equation y' = (2y)/t?
11. ### Family and the role and nature of the 'index'

I am seekinhg to understand example 4 on page 9 of Cohn's book "Introduction to Ring Theory" The example needs a clear understanding of the nottion of a family which Cohn briefly introduces on page 3 where he defines the notion of a set and members of a set and then defines a family mentioning...
12. ### Family of monotonic strictly increasing functions...

Definitions: For functions f,g:N→N, we say f≤∗g if there exist n∈N such that for n≤m we have f(m)≤g(m) Family F of functions from N to N is unbounded if for every function g:N→N, exist f∈Fsuch that f≤∗g isn't holds. Question: F is unbounded family of monotonic strictly increasing functions...
13. ### Proving union and intersection of indexed family of sets

I have to prove that the union for n an element of the natural numbers of the indexed set D=(-n,1/n) is equal to (-infinity,1). And that the intersection for n an element of the natural numbers of the indexed set D=(-n,1/n) is equal to (-1,0]. I've asked the professor twice now for help and he...

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15. ### Beta Family Distribution

Hi everyone, i'm a student of University of Indonesia, mathematics majoring. I have a problem to find out how to prove that for the condition on the attachment, the beta distribution can transform to be another type of distribution. I really need help on it, because my mathematical proofing is...
16. ### Creation of a General Formula for a family of Curve Shapes

I have a process that requires an operational profile that follows one of the curves in the diagram which follows. I wish to program into the device a general equation that will give me a family of curves of this general shape. The goal is to adjust the parameters of the equation so that I can...
17. ### Creation of a General Formula for a family of Curve Shapes

I have a process that requires an operational profile that follows one of the curves in the diagram which follows. I wish to program into the device a general equation that will give me a family of curves of this general shape. The goal is to adjust the parameters of the equation so that I can...
18. ### Product of two discrete distributions is one of the same family?

Hi, I have this problem with which I could do with some help. Given the marginal pdfs shown below, find the pdf of X + Y (given X and Y are independent). p_{X}(k) = \exp{(- \lambda)} \cdot \frac{\lambda^k}{k!} and p_{Y}(k) = \exp{(- \mu)} \cdot \frac{\mu^k}{k!} where k = 1, 2, 3,\ldots I...
19. ### union and intersection of family sets

Solved! union and intersection of family sets Hi there I'm new here, but I guess I'm going to ask many questions in the future. I'm trying to study mathematics on my own, but I need some help to make sure I'm understanding the concepts correctly... Anyways, here is my first problem. I'm...
20. ### A family of operators with a specific property

Hi! I'm stuck trying to solve the below stated problem. (Any suggestions and help is more than welcome). Thanks! PROBLEM: Define T_b by T_b f(t)=bf(t) (where f(t)\in L^p([0,1]) and 1\leq p fixed). The task is to find all bounded linear maps T from L^p([0,1]) to L^p([0,1]) with the property...