Q.7.33 If E[X]=1and Var(X)=5聽find(a)聽... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 7: Q.7.33 (page 354)

If $E [X] = 1$ and $V a r (X) = 5$ find
(a) $E [(2 + X^{2})]$
(b) $V a r (4 + 3 X)$

Short Answer

Expert verified

a) The value of $E [(2 + X^{2})]$ is $14$ .

b) The value of $Var (4 + 3 X)$ is $45 .$

Step by step solution

Given information (Part a)

$E (X) = 1$

$V a r (X) = 5$

Then $E [(2 + X^{2})] = ?$

Explanation (Part a)

We know that

$E (X^{2}) = Var (X) + (E (X))^{2}$

$= 5 + 1$

$= 6$

Calculate the expected value of $E [(2 + X^{2})]$

$E [(2 + X)^{2}] = E [4 + X^{2} + 4 X]$

$= 4 + 6 + 4$

$= 14$

Final Answer (Part a)

The value of $E [(2 + X^{2})]$ is $14 .$

Given information (Part b)

$E (X) = 1$

$Var (X) = 5$

Then $Var (4 + 3 x) = ?$

Explanation (Part b)

We know that,

$E (X^{2}) = Var (X) + (E (X))^{2}$

$= 5 + 1$

role="math" localid="1647519062218" $= 6$

Calculate the variance.

$V a r (4 + 3 X) = 0 + 9 V a r (X)$

$= (9 脳 5)$

$= 45$

Final Answer (Part b)

Hence, the value of $V a r (4 + 3 x)$ is $45 .$

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91影视

If $E [X] = 1$ and $V a r (X) = 5$ find
(a) $E [(2 + X^{2})]$
(b) $V a r (4 + 3 X)$

Short Answer

Step by step solution

Given information (Part a)

Explanation (Part a)

Final Answer (Part a)

Given information (Part b)

Explanation (Part b)

Final Answer (Part b)

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91影视

If E[X]=1and Var(X)=5find(a)E[(2+X2)](b)Var(4+3X)

Short Answer

Step by step solution

Given information (Part a)

Explanation (Part a)

Final Answer (Part a)

Given information (Part b)

Explanation (Part b)

Final Answer (Part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Pure Maths

Statistics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

If $E [X] = 1$ and $V a r (X) = 5$ find
(a) $E [(2 + X^{2})]$
(b) $V a r (4 + 3 X)$