A research team studies the probability of crop damage by wild boar in crop fields. For each crop field sampled, they record 1 if damage was observed, and 0 if damage was not observed. Which one of the following distributions is most appropriate to analyse the probability of crop damage?
Show Hint
- Binomial distribution
- Poisson distribution
- Cauchy distribution
- Gamma distribution
The Correct Option is A
Solution and Explanation
Each field produces a binary outcome: damaged \(=1\) or not damaged \(=0\). For a single field this is a Bernoulli trial with success probability \(p=\Pr(\text{damage})\).
Step 2: Aggregate across many fields.
If \(n\) independent fields are observed under similar conditions, the total number of damaged fields \(X\) follows \[ X \sim \text{Binomial}(n,p), \] because \(X\) is the sum of \(n\) independent Bernoulli(\(p\)) variables. Inference for \(p\) (including proportion estimates and logistic models) uses the binomial likelihood.
Step 3: Eliminate other options.
Poisson models counts of events in continuous space/time with rate parameter; not appropriate for fixed-\(n\) binary trials.
Cauchy is a continuous distribution with heavy tails; irrelevant here.
Gamma is continuous on \((0,\infty)\); used for waiting times or positive continuous quantities, not binary outcomes. Final Answer:
\[ \boxed{\text{(A) Binomial distribution}} \]
Top Questions on Probability distributions
The probability distribution of a random variable X is given by
X 0 1 2 P(X) \(1 - 7a^2\) \(\tfrac{1}{2}a + \tfrac{1}{4}\) \(a^2\)
If \(a > 0\), then \(P(0 < X \leq 2)\) is equal to- CUET (UG) - 2025
- Mathematics
- Probability distributions
- The probability distribution of a random variable X is given by
\begin{tabular}{|c|c|c|c|} \hline X & 0 & 1 & 2 \\ \hline P(X) & $1 - 7a^2$ & $\frac{1}{2}a + \frac{1}{4}$ & $a^2$ \\ \hline \end{tabular}
If a > 0, then P(0 $<$ x $\le$ 2) is equal to- CUET (UG) - 2025
- Mathematics
- Probability distributions
- A bird eats two types of worms, P and Q, picking them randomly. Which one of the following describes the kind of probability distribution of the number of worms of type P eaten by the bird in a day?
- GATE EY - 2025
- Mathematics
- Probability distributions
The mean of the density function is \(f(x) = \lambda e^{-\lambda x}, x > 0\) is ____ .
- AP PGECET - 2024
- Mathematics
- Probability distributions
Questions Asked in GATE EY exam
Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.
Abuse \( \rightarrow \) Insult \( \rightarrow \) Ridicule
__________ \( \rightarrow \) Praise \( \rightarrow \) Appreciate
- Which one of the following mechanisms is expected to generate tightly linked genes?
- GATE EY - 2025
- Genetics
- An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee.
The overhead is 20% of the consulting fee if the fee is up to ₹5,00,000.
For higher fees, the overhead is ₹1,00,000 plus 10% of the amount by which the fee exceeds ₹5,00,000.
The government charges a Goods and Services Tax (GST) of 18% on the total amount (i.e., the consulting fee plus the overhead).
An employee of the organization charges this entire amount — that is, the consulting fee, overhead, and tax — to the client.
If the client cannot pay more than ₹10,00,000, what is the maximum consulting fee that the employee can charge? The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?