Suppose that X_{1}, X_{2} and X_{3} are three independent random variables with the same distribution as X. What is the ecpected value of the sum X_{1

Rui Baldwin

Rui Baldwin

Answered question

2021-05-12

Suppose that X1,X2 and X3 are three independent random variables with the same distribution as X.
What is the expected value of the sum X1+X2+X3? The product X1X2X3?
Suppose a discrete random variable X assumes the value 32 with probability 0.5 and assumes the value 12 with probability 0.5.

Answer & Explanation

Arham Warner

Arham Warner

Skilled2021-05-13Added 102 answers

Step 1
The expectation of X is as follows:
E(X)=μ
=xP(X=x)
=32×(0.5)+12×(0.5)
=1
Step 2
The random variables X1,X2,andX3 are independent and have the same the distribution of X. The required expectations are calculated as follows:
E(X1+X2+X3)=E(X1)+E(X2)+E(X3)
=E(X)+E(X)+E(X)
=3E(X)
=3×1
=3
E(X1X2X3)=E(X1)×E(X2)×E(X3)
=E(X)×E(X)×E(X)
=1×1×1
=1

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