If X is a Poisson variate such that 3P(X=2)=2P(X=1), then P(X=0) is equal to: (Given e^(-4/3)=0.264) Option 1: 0.528 Option 2: 0.264 Option 3: 0.132 Option 4: 0.204

Answer: 0.264. Solution: For a Poisson variate, P(X=r) = (e^(-)^r)/(r!). 3*(e^(-)^2)/2 = 2e^(-) gives (3)/2 = 2, so = 4/3. Then P(X=0) = e^(-4/3) = 0.264.

Applied Mathematics

Probability Distribution

Medium

applied

If X is a Poisson variate such that $3P(X=2)=2P(X=1)$ , then $P(X=0)$ is equal to: (Given $e^{-4/3}=0.264$ )

0.528

0.264

0.132

0.204

✅ Correct Option: 2

For a Poisson variate, $P(X=r) = \dfrac{e^{-\lambda}\lambda^r}{r!}$ .

$3\cdot\dfrac{e^{-\lambda}\lambda^2}{2} = 2e^{-\lambda}\lambda$ gives $\dfrac{3\lambda}{2} = 2$ , so $\lambda = \dfrac{4}{3}$ .

Then $P(X=0) = e^{-4/3} = 0.264$ .

2026: 29 May Shift 2

The probability distribution of a discrete random variable is given below :

X	1	2	3	4	5
P(X)	1/5	m	2/5	2m	3m

Which of the following are correct?

A. $P(2)=\frac{1}{15}$

B. $P(4)=\frac{2}{15}$

C. $P(X<2)=\frac{1}{5}$

D. $P(X\geq4)=\frac{1}{5}$

Choose the correct answer from the options given below:

2022: 25 May Shift 1

If the probability distribution of a discrete random variable $X$ is given as

X	0	1	2	3	4
P(X)	0.5	2k	3k	3k	2k

Then the value of $k$ is:

2023: 11 Aug Shift 1

2 voices dice are thrown together. For the first die $P(6) = \frac{1}{2}$ , other scores are equally likely. While for the second die $P(1) = \frac{2}{5}$ and other scores are equally likely than the Mean for the probability distribution of the number of one score will be

2023: 7 June Shift 1

Match List - I with list- II

List-I	List - II
A. the probability distribution is applied for discrete random variable	normal distribution
B. A normal distribution is symmetric about	standard deviation
C. this probability distribution is applied for continuous random variable	mean
D. the shape of normal curve depend upon	Poisson distribution

Choose the correct option below :

2026: 30 May Shift 2

In a printing press of a publication house, there is a small chance $\frac{1}{1000}$ for any typing error in 20 pages, then the number of pages containing no error in printing two volumes of an Encyclopedia containing total 10000 pages are:

[Given: $e^{-0.02}=0.9802$ ]

2023: 23 May Shift 3

If the mean of a binomial distribution is 12 and its standard deviation is 2, then the number of trials is :

If X is a Poisson variate such that 3P(X=2)=2P(X=1)3P(X=2)=2P(X=1)3P(X=2)=2P(X=1), then P(X=0)P(X=0)P(X=0) is equal to: (Given e−4/3=0.264e^{-4/3}=0.264e−4/3=0.264)

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If X is a Poisson variate such that $3P(X=2)=2P(X=1)$ , then $P(X=0)$ is equal to: (Given $e^{-4/3}=0.264$ )