CUET · MATHS · PYQ PAPER 2025
If the random variable \(X\) follows the Poisson distribution such that \(P(X=k)=P(X=k+1)\), then the mean value of \(X\) is :
- A \(k\)
- B \(k-1\)
- C \(k^2\)
- D \(k+1\)
Answer & Solution
Correct Answer
(D) \(k+1\)
Step-by-step Solution
Detailed explanation
\(\frac{e^{-\lambda} \lambda^k}{k!} = \frac{e^{-\lambda} \lambda^{k+1}}{(k+1)!}\) \(\frac{1}{k!} = \frac{\lambda}{(k+1)k!}\) \(1 = \frac{\lambda}{k+1}\) \(\lambda = k+1\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- The area (in sq. units) of the region bounded by \(y=2 \sqrt{1-x^2}, x \in[0,1]\) and \(x\)-axis is equal to:CUET 2025 Hard
- For \(x>e\),\(\int \frac{d x}{x-\sqrt{x}}\) is equal toCUET 2025 Hard
- The value of \(3^{18}(\bmod 4)\) is equal toCUET 2025 Easy
- If \(f(x)=\left\{\begin{array}{l}m x+1, x \geq \pi / 2 \\ \sin x+n, x \leq \pi / 2\end{array}\right.\) is continuous at \(x=\pi / 2\), where \(m \in Z\) (set of integers), then \(\sin 2 n=\)CUET 2025 Easy
- If \( \vec{a}\) is a unit vector and \((\vec{x}-\vec{a}) \cdot(\vec{x}+\vec{a})=15\), then the value of \(|\vec{x}|\) is :CUET 2025 Medium
- If \(\theta \in[0, \pi]\) is the angle between any two non-zero vectors \(\vec{a}\) and \(\vec{b}\), such that \(|\vec{a} \cdot \vec{b}|=|\vec{a} \times \vec{b}|\), then \(\theta=\)CUET 2023 Easy
More PYQs from CUET
- Based on the data available for the production ( \(y_i\) in thousand tons) of a cloth factory for 7 years (\(x_i\)) using the method of least squares, the straight line trend is given by \(y=a+b x\) with \(\sum y_i=608, \sum x_i=0, \sum x_i y_i=116, \sum x_i^2=28\). Then, the increase in production per year is :CUET 2025 Medium
- Trichoderma species is:
(A) Free living fungi
(B) Very common in the root ecosystem
(C) Effective biocontrol agent
(D) Resistance to insects
Choose the correct answer from the options given below:CUET 2025 Hard - Match List I with List II
Choose the correct answer from the options given below:List - I List - II (A) Convergent evolution (I) Speciation (B) Divergent evolution (II) Analogous organs (C) Adaptive radiation (III) Homologous organs (D) Natural selection (IV) Australian marsupials CUET 2023 Medium - The demand function for a commodity is \(p=35-2 x-x^2\), then the consumer's surplus at equilibrium price \(p_0=20\) isCUET 2025 Easy
- If \(\vec{a}=\hat{i}+2 \hat{j}+2 \hat{k},|\vec{b}|=5\) and the angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{\pi}{6}\), then the area of the triangle formed by these two vectors as two sides is :CUET 2023 Easy
- A nucleoside comprises:CUET 2023 Easy