Question

Match List-I with List-II. List-I: A. Poisson distribution \(P(x=r)\), B. Mean \((\mu)\), C. Standard deviation \((\sigma)\), D. Binomial distribution.

• A. A-I, B-II, C-III, D-IV
• B. A-II, B-I, C-IV, D-III
• C. A-I, B-II, C-IV, D-III
• D. A-II, B-I, C-III, D-IV

Hint:

For binomial distribution, mean is \(np\) and standard deviation is \(\sqrt{npq}\). For Poisson distribution, \(P(x=r)=\frac{e^{-m}m^r}{r!}\).

Answer 1

The Correct Option is B

Concept:
This question is based on probability distributions and their standard formulas. Poisson and binomial distributions are common discrete probability distributions.

Step 1: Formula for mean.
For binomial distribution, the mean is: \[ \mu = np \] So, \[ B \rightarrow I \]

Step 2: Formula for standard deviation.
For binomial distribution, the standard deviation is: \[ \sigma = \sqrt{npq} \] So, \[ C \rightarrow IV \]

Step 3: Formula for Poisson distribution.
The probability mass function of Poisson distribution is: \[ P(x=r)=\frac{e^{-m}m^r}{r!} \] So, \[ A \rightarrow II \]

Step 4: Formula for binomial distribution.
The probability mass function of binomial distribution is: \[ P(X=r)=\,^nC_rp^rq^{n-r} \] So, \[ D \rightarrow III \] Therefore, the correct matching is: \[ A-II,\ B-I,\ C-IV,\ D-III \] \[ \therefore \text{Correct Answer is (B)} \]