A random variable X follows Poisson distribution. The variance of X is 2. The value of P(X=3) is Option 1: 3/4e^2 Option 2: 4/3e^2 Option 3: 3e^2/4 Option 4: 4e^2/3

The answer is '4/3e^2'. View full solution:

CUET Mathematics - A random variable X follows Poisson distribution. The variance of X is 2. The value of P(X=3) is | PYQs + Solutions

CUET Mathematics 2026 21st May Shift 2

Applied Mathematics

Easy

applied

$\dfrac{3}{4e^2}$

$\dfrac{4}{3e^2}$

$\dfrac{3e^2}{4}$

$\dfrac{4e^2}{3}$

✅ Correct Option: 2

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22nd 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.

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19th May Shift 2

If $X$ is a discrete random variable which assumes values $x_1, x_2, x_3, ..., x_n$ with the respective probabilities $p_1, p_2, ....., p_n$ , then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\displaystyle\sum_{i=1}^{n} p_i =$	I.	$E(X^2)$
B.	$\displaystyle\sum_{i=1}^{n} p_i x_i =$	II.	$Var(X)$
C.	$\displaystyle\sum_{i=1}^{n} p_i x_i^2 =$	III.	$1$
D.	$E(X^2) - \{E(X)\}^2 =$	IV.	$E(X)$

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29th May Shift 2

If 0.1% of the bolts manufactured by a machine are found to be defective. Find the probability that, in a sample of 2000 bolts chosen at random, exactly 3 will be defective using the Poisson distribution. [Given $e^{-2} =0.1353$ ]

CUET Mathematics 2026 21st May Shift 2 PYQs

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