Question:
A random variable X takes the values 0, 1, 2, 3 and its mean is \(1.3\). If \(P(X=3)=2P(X=1)\) and \(P(X=2)=0.3\), then \(P(X=0)\) is
A random variable X takes the values 0, 1, 2, 3 and its mean is \(1.3\). If \(P(X=3)=2P(X=1)\) and \(P(X=2)=0.3\), then \(P(X=0)\) is
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Use that probabilities sum to 1 and the mean equals 1.3 to get two equations, then solve.
Updated On: Nov 12, 2026
- \(0.2\)
- \(0.1\)
- \(0.3\)
- \(0.4\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
Let \(P(X=1)=p\). Then \(P(X=3)=2p\) and \(P(X=2)=0.3\).
Step 2: Use the mean
\(E(X)=1\cdot p+2(0.3)+3(2p)=7p+0.6=1.3\Rightarrow p=0.1\).
Step 3: Use the total probability
\(P(X=3)=0.2\).
Sum of probabilities: \(P(X=0)+0.1+0.3+0.2=1\).
Step 4: Result
\(P(X=0)=1-0.6=0.4\).
Final Answer:
P(X = 0) equals 0.4. \[ \boxed{\text{(D) }0.4} \]
Let \(P(X=1)=p\). Then \(P(X=3)=2p\) and \(P(X=2)=0.3\).
Step 2: Use the mean
\(E(X)=1\cdot p+2(0.3)+3(2p)=7p+0.6=1.3\Rightarrow p=0.1\).
Step 3: Use the total probability
\(P(X=3)=0.2\).
Sum of probabilities: \(P(X=0)+0.1+0.3+0.2=1\).
Step 4: Result
\(P(X=0)=1-0.6=0.4\).
Final Answer:
P(X = 0) equals 0.4. \[ \boxed{\text{(D) }0.4} \]
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