If X has a Poisson distribution such that P(X = 1) = P(X = 2) then P(X = 3) is : Option 1: 4/3 e^(-2) Option 2: 1/3 e^(-3) Option 3: 2/3 e^(-2) Option 4: 5/3 e^(-4)

Answer: 4/3 e^(-2). Solution: P(X=1) = P(X=2): e^(-) = (^2)/2e^(-), so = 2. Then P(X=3) = (2^3 e^(-2))/(3!) = 8/6e^(-2) = 4/3e^(-2).

Applied Mathematics

Probability Distribution

Medium

applied

If X has a Poisson distribution such that $P(X = 1) = P(X = 2)$ then $P(X = 3)$ is :

$\frac{4}{3} e^{-2}$

$\frac{1}{3} e^{-3}$

$\frac{2}{3} e^{-2}$

$\frac{5}{3} e^{-4}$

✅ Correct Option: 1

$P(X=1) = P(X=2)$ : $\lambda e^{-\lambda} = \frac{\lambda^2}{2}e^{-\lambda}$ , so $\lambda = 2$ . Then $P(X=3) = \frac{2^3 e^{-2}}{3!} = \frac{8}{6}e^{-2} = \frac{4}{3}e^{-2}$ .

2026: 21 May Shift 2

The random variable X has a probability distribution $P(X)$ of the following form, where $k$ is some real number.

$P(X=x) = \begin{cases}k, & \text{if } x=0\\\dfrac{k}{2}, & \text{if } x=1 \text{ or } 2\\0, & \text{otherwise}\end{cases}$

On the basis of the above information, match List-I with List-II

LIST-I		LIST-II
A. Value of $k$		I. $\dfrac{1}{4}$
B. $P(X<2)$		II. 0
C. $P(X>1)$		III. $\dfrac{1}{2}$
D. $P(X>2)$		IV. $\dfrac{3}{4}$

Choose the correct answer from the options given below:

2026: 30 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Mean of a normal variate X is 12 and standard deviation is 4, then the Z-score of data point 20 is	(I) 1
(B) If X is Poisson variate such that P(X=1) = 2P(X=2), then the mean of X is	(II) 8
(C) In a binomial distribution, if mean is 5 and variance is 4, then the number of trials is	(III) 2
(D) In a binomial distribution, if n = 20 and q = 0.6, then its mean is	(IV) 25

Choose the correct answer from the options given below:

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. The variance of a Poisson distribution with mean $\lambda$ is	I. $\sqrt{\lambda}$
B. The standard deviation of a Poisson distribution with mean $\lambda$ is	II. 4
C. In a Poisson distribution, if mean is 4, then the standard deviation is	III. $\lambda$
D. In a Poisson distribution, if mean is 4, then the variance is	IV. 2

Choose the correct answer from the options given below:

2023: 23 May Shift 3

A book consisting of 2000 pages has 540 misprints distributed randomly throughout the book. The average number of misprints in one page of the book is:

2026: 12 May Shift 2

If a coin is tossed 8 times and getting a head is considered as success, then which of the following statements are correct ?

(A) The probability of getting 4 heads is $\dfrac{35}{128}$

(B) The mean of the number of successes is 4.

(D) The probability of getting 6 heads is $\dfrac{9}{64}$ .

Choose the correct answer from the options given below:

2023: 23 May Shift 3

The variance of the Binomial Distribution $B\left(5, \frac{1}{4}\right)$ is:

If X has a Poisson distribution such that P(X=1)=P(X=2)P(X = 1) = P(X = 2)P(X=1)=P(X=2) then P(X=3)P(X = 3)P(X=3) is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If X has a Poisson distribution such that $P(X = 1) = P(X = 2)$ then $P(X = 3)$ is :