If probability distribution is given by,
| x | 0 | 1 | 2 | 3 |
| p(x) | b |
Correct Answer :
Solution :
The correct option is .
To find the value of , we utilize two key properties of probability distributions.
Step 1: Use the property that the total probability must equal 1.
The sum of all probabilities in a discrete probability distribution is always equal to 1:
(Equation 1)
Step 2: Use the formula for variance and mean.
We are given that .
Recall that the variance is defined as:
Step 3: Solve the system of linear equations for a and b.
Multiply Equation 1 by 3 to match the coefficient of b in Equation 2:
Step 4: Compute the ratio .
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