Since P\left\{x=-1\right\} = P \left\{x=1\right\} = 1/2 , calculate the expected value and variance of the X random variable. E \left[(X + 1)^{2}\right] =?

lwfrgin 2021-01-08 Answered

Since Px=1=Px=1=12 , calculate the expected value and variance of the X random variable.
E[(X+1)2]=?

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Expert Answer

Neelam Wainwright
Answered 2021-01-09 Author has 102 answers

Step 1
Solution:
From the given information,
P{x=1t}=12
P{x=1}=12
Step 2
Then, the expected value of the X random variable is
E(X)=xP(x)
=(1)×12+(1×12)=0
Thus, the expected value of the X random variable is 0.
Step 3
E(X2)=x2P(x)
=((1)2×12)+(12×12)
=12+12=1
Then, the variance of the X random variable is
V(X)=E(X2){E(X)}2
=102=1
Thus, the variance of the X random variable is 1.
Step 4
E[(X+1)2]=E[X2+2X+1]
=E[X2]+2E[X]+E[1]
=1+2(0)+1=2

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Jeffrey Jordon
Answered 2021-11-17 Author has 2064 answers

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