Chapter 4: Q. 4.1 (page 173)

Suppose that the random variable $X$ is equal to the number of hits obtained by a certain baseball player in his next $3$ at-bats. If $P {X = 1} = 3, P {X = 2} = 2$ and $P {X = 0} = 3 P {X = 3}$ , find $E [X] .$

Short Answer

Expert verified

The value of $E [X]$ is $= 1.075 .$

Step by step solution

Given Information

Given in the question that,

$P (X = 1) = 0.3$

$P (X = 2) = 0.2$

$P (X = 0) = 3 P (X = 3)$

Solution of the Problem

We know that

$P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) = 1$

$0.5 + 4 P (X = 3) = 1$

Find the value,

$P (X = 3) = 0.125$

$P (X = 0) = 3 \times 0.125 = 0.375$

Computation of the Value

Find the value

\begin{array}{l} X_{i} & P_{i} \\ 0 & 0.375 \\ 1 & 0.3 \\ 2 & 0.2 \\ 3 & 0.125 \end{array}

$E (X) = \sum x_{i} p_{i}$

$= 0 \times 0.375 + 1 \times 0.3 + 2 \times 0.2 + 3 \times 0.125$

$= 1.075 .$

Final Answer

The value of $E (X)$ is $1.075 .$ $1.075 .$

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Suppose that the random variable $X$ is equal to the number of hits obtained by a certain baseball player in his next $3$ at-bats. If $P {X = 1} = 3, P {X = 2} = 2$ and $P {X = 0} = 3 P {X = 3}$ , find $E [X] .$

Short Answer

Step by step solution

Given Information

Solution of the Problem

Computation of the Value

Final Answer

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Suppose that the random variable Xis equal to the number of hits obtained by a certain baseball player in his next 3at-bats. If P{X=1}=3,P{X=2}=2andP{X=0}=3P{X=3}, find E[X].

Short Answer

Step by step solution

Given Information

Solution of the Problem

Computation of the Value

Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Calculus

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Suppose that the random variable $X$ is equal to the number of hits obtained by a certain baseball player in his next $3$ at-bats. If $P {X = 1} = 3, P {X = 2} = 2$ and $P {X = 0} = 3 P {X = 3}$ , find $E [X] .$