Y is a random variable that takes value 10X has binomial distribution, with n = 20 and π =with probability and 5 with remaining probability. Finally, c is a constant equal to 3. What isthe value of E[X + Y + c]?15231141/4

Given that The random variable X is binomial X~Bn=20,π=14 The random variable Y is f(y)=25…

X has binomial distribution, with n = 20 and π = 1. Y is a random variable that takes value 10 with probability and 5 with remaining probability. Finally, c is a constant equal to 3. What is the value of E[X + Y + c]? 15 23 7 11 41/4

X has binomial distribution, with n = 20 and π = 1. Y is a random variable that takes value 10 with probability and 5 with remaining probability. Finally, c is a constant equal to 3. What is the value of E[X + Y + c]? 15 23 7 11 41/4

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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Question

100%

Y is a random variable that takes value 10
X has binomial distribution, with n = 20 and π =
with probability and 5 with remaining probability. Finally, c is a constant equal to 3. What is
the value of E[X + Y + c]?
15
23
11
41/4

Expert Solution

Step 1

Given that

The random variable $X$ is binomial

$X ~ B (n = 20, π = \frac{1}{4})$

The random variable $Y$ is

$\begin{array}{rcl} f (y) & = & \frac{2}{5}, X = 10 \\ = & 1 - \frac{2}{5}, X = 5 \end{array}$

The constant $C$ is 3

The formula for the expected value is

$E (X) = \sum_{}^{} x P (X = x)$

The expected value of the binomial distribution is $n π$

The expected value of the sum of two random variables is the sum of the expected value of individual random variables.

The expected value of the constant is constant.

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