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Home Question Bank Math Probability Archive 2024 December 19

Probability Questions from Dec 19,2024

Browse the Probability Q&A Archive for Dec 19,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Se a probabilidade de um evento A ocorrer é 0,3 e a probabilidade de um evento B ocorrer é 0,5, quais são as chances de ambos os eventos ocorrerem se eles forem independentes? 1. The numbers 1 through 15 were each written on individual pieces of paper, 1 number per piece. Then the 15 pieces of paper were put in a jar. One piece of paper will be drawn from the jar at random. What is the probability of drawing a piece of paper with a number less than 9 written on it? Completar el siguiente enunciado: Un es una representación gráfica de los posibles resultados de un experimento que tiene varios pasos. a. diagrama de árbol b. caso favorable d. conento simple Calculate the probability density function from the probability distribution function given below. \[ f x(x)=\left\{\begin{array}{cc}0 & x \leq 0 \\ x^{2} & 0<x \leq 1 \\ 1 & 1<x\end{array}\right. \] Exercice 1 Soit \( (X, Y) \) un couple aléatoire à valeurs dans \( \mathbb{R}^{2} \) admettant la densité 1. Déterminer \( C \) \begin{tabular}{l|l|l|l} Déterminer \( C \) \\ Calculer les lois marginales. En déduire que \( X \) et \( Y \) ne sont pas indépendántes. \\ Calculer \( P(X+Y \leqslant 0) \) et \( P(X \leqslant 0, Y \leqslant 0) \)\end{tabular} b) Let the random variable \( (\mathrm{X}, \mathrm{Y}) \) have the joint probability density function \( f_{X, Y}(x, y)=\exp \{-(x+y)\}, x>0, y>0 \). i. Derive the marginal probability density functions of \( X \) and \( Y \), and hence determine (giving reasons) whether or not the two variables are independent ii. Derive the joint cumulative distribution function \( F_{X, Y}(x, y) \) i. Derive the marginal probability density functions of X and Y , and hence determine (giving reasons) whether or not the two variables are independent ii. Derive the joint cumulative distribution function \( F_{X, Y}(x, y) \) a) Suppose that \( f(x)=e^{-(x-4)} \) for \( 4<x \). Determine the following probabilities i. \( P(1<X) \) ii. \( \quad P(2 \leq X \leq 5) \) iii. \( \quad P(5<X) \) iv. \( \quad \begin{array}{l}\text { Determine } x \text { such that } P(X<x)=0.90 \\ \text { v. }\end{array} \quad \) Determine the cumulative distribution function for the distribution, \( f(x) \) b) Suppose that the time it takes a data collection operator to fill out an electronic form for a database is uniformly between 1.5 and 2.2 minutes i. What is the probability that it will take less than two minutes to fill out the form? ii. Determine the cumulative distribution function of the time it takes to fill out the form
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