Let the random variable X follow a Poisson distribution. If P(X=3)=2/5P(X=2), then P(X=1) is equal to Option 1: 6/5e^(-6/5) Option 2: 6/5e^(-5/6) Option 3: 5/6e^(-6/5) Option 4: 5/6e^(-5/6)

Answer: 6/5e^(-6/5). Solution: Using P(X=k)=(e^(-)^k)/(k!), the condition gives (^3)/6=2/5 * (^2)/2, so ()/6=1/5 and =6/5. Then P(X=1)= e^(-)=6/5e^(-6/5).

Applied Mathematics

Probability Distribution

Medium

applied

Let the random variable $X$ follow a Poisson distribution. If $P(X=3)=\dfrac{2}{5}P(X=2)$ , then $P(X=1)$ is equal to

$\dfrac{6}{5}e^{-\frac{6}{5}}$

$\dfrac{6}{5}e^{-\frac{5}{6}}$

$\dfrac{5}{6}e^{-\frac{6}{5}}$

$\dfrac{5}{6}e^{-\frac{5}{6}}$

✅ Correct Option: 1

Using $P(X=k)=\frac{e^{-\lambda}\lambda^k}{k!}$ , the condition gives $\frac{\lambda^3}{6}=\frac{2}{5} \cdot \frac{\lambda^2}{2}$ , so $\frac{\lambda}{6}=\frac{1}{5}$ and $\lambda=\frac{6}{5}$ . Then $P(X=1)=\lambda e^{-\lambda}=\frac{6}{5}e^{-\frac{6}{5}}$ .

2026: 29 May Shift 2

In a binomial distribution, the sum of its mean and variance is 1.8. If the event was conducted 5 times, then the probability of 3 successes is

2026: 21 May Shift 2

If a random variable X follows binomial distribution with mean $\dfrac{4}{3}$ and variance $\dfrac{8}{9}$ . Which of the following are correct?

A. Probability of success is $\dfrac{1}{3}$ .

B. Probability of failure is $\dfrac{2}{3}$ .

C. Number of trials is 4.

D. $P(X \ge 1) = \dfrac{35}{81}$

Choose the correct answer from the options given below:

2026: 22 May Shift 2

If the heights of 300 students are normally distributed with mean 68 inches and standard deviation 3 inches. If Z is the standard normal variate such that $P(0\le Z\le 1.33)=0.4082, P(Z\ge 1.33)=0.0918$ and $P(0\le Z\le 1)=0.3413$ , then which of the following statements are correct?

(A) There are 27 students whose height is greater than 72 inches.

(B) The number of students having heights less than or equal to 64 inches is 27.

(D) There are 35 students whose height is greater then 72 inches.

Choose the correct answer from the options given 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: $e^{-0.02}=0.9802$ ]

2026: 21 May Shift 2

In a single throw of a die, if X denotes the number on its upper face, then the mean of X 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

Let the random variable XXX follow a Poisson distribution. If P(X=3)=25P(X=2)P(X=3)=\dfrac{2}{5}P(X=2)P(X=3)=52​P(X=2), then P(X=1)P(X=1)P(X=1) is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Let the random variable $X$ follow a Poisson distribution. If $P(X=3)=\dfrac{2}{5}P(X=2)$ , then $P(X=1)$ is equal to