Question

The probability mass function (p.m.f) of a random variable \(X\) is \(p(x)=\frac{x+3}{k},x=-2,-1,0,1\) and \(p(x)=0\) otherwise, then the value of \(E(x)=...\)

• A. \(0\)
• B. \(1\)
• C. \(2\)
• D. \(-1\)

Hint:

First find k from the sum of probabilities being 1, then compute the sum of x times p(x).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The probabilities must add to 1.

Step 2: Find k
\(\dfrac{1+2+3+4}{k}=1\Rightarrow k=10\).
So \(p(-2)=\dfrac1{10},\ p(-1)=\dfrac2{10},\ p(0)=\dfrac3{10},\ p(1)=\dfrac4{10}\).

Step 3: Expected value
\(E(X)=\sum xp(x)=\dfrac{-2(1)-1(2)+0(3)+1(4)}{10}\).

Step 4: Evaluate
\(E(X)=\dfrac{-2-2+0+4}{10}=0\).

Final Answer:
The expected value is 0. \[ \boxed{\text{(A) }0} \]