4.2-4 The image contains a mathematics problem related to trinomial distribution involving variables $X$ and $Y$.**Problem 4.2-4:**Let $X$ and $Y$ have a trinomial distribution with parameters $n = 3$, $p_X = 1/6$, and $p_Y = 1/2$. Find:(a) $E(X)$.(b) $E(Y)$.(c) $\text{Var}(X)$.(d) $\text{Var}(Y)$.(e) $\text{Cov}(X, Y)$.(f) $\rho$.Note that $\rho = -\sqrt{p_X p_Y / (1 - p_X)(1 - p_Y)}$ in this case.(Indeed, the formula holds in general for the trinomial distribution; see Example 4.3-3.)**Problem 4.2-5:**Let $X$ and $Y$ be random variables with respective means $\mu_X$ and $\mu_Y$, respective variances $\sigma_X^2$ and $\sigma_Y^2$, and correlation coefficient $\rho$. Fit the line $y = a + bx$ by the method of least squares to the probability distribution by minimizing the expectation...

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Description: 4.2-4 The image contains a mathematics problem related to trinomial distribution involving variables $X$ and $Y$.**Problem 4.2-4:**Let $X$ and $Y$ have a trinomial distribution with parameters $n = 3$, $p_X = 1/6$, and $p_Y = 1/2$. Find

Solution: Given information Let X and Y have trinomial distribution with parameters n= 3, px=16…

Answered: 4.2-4. Let X and Y have a trinomial…

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4.2-4. Let X and Y have a trinomial distribution with parameters n= 3, px = 1/6, and py = 1/2. Find (a) E(X). (b) E(Y). (c) Var(X). (d) Var(Y). (e) Cov(X, Y). () p.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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4.2-4

The image contains a mathematics problem related to trinomial distribution involving variables $X$ and $Y$.

**Problem 4.2-4:**
Let $X$ and $Y$ have a trinomial distribution with parameters $n = 3$, $p_X = 1/6$, and $p_Y = 1/2$. Find:

(a) $E(X)$.

(b) $E(Y)$.

(c) $\text{Var}(X)$.

(d) $\text{Var}(Y)$.

(e) $\text{Cov}(X, Y)$.

(f) $\rho$.

Note that $\rho = -\sqrt{p_X p_Y / (1 - p_X)(1 - p_Y)}$ in this case.

(Indeed, the formula holds in general for the trinomial distribution; see Example 4.3-3.)

**Problem 4.2-5:**
Let $X$ and $Y$ be random variables with respective means $\mu_X$ and $\mu_Y$, respective variances $\sigma_X^2$ and $\sigma_Y^2$, and correlation coefficient $\rho$. Fit the line $y = a + bx$ by the method of least squares to the probability distribution by minimizing the expectation...

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