The probability distribution of a random variable X is given below :, X, 0, 1, 2, 3, 4, P(X), 0.1, 0.25, 0.3, 0.2, 0.15, Then, Var(X/2) is : Option 1: 0.368751 Option 2: 0.361875 Option 3: 0.36758 Option 4: 0.369822

Answer: 0.361875. Solution: E(X) = 0(0.1) + 1(0.25) + 2(0.3) + 3(0.2) + 4(0.15) = 2.05. E(X^2) = 0 + 0.25 + 1.2 + 1.8 + 2.4 = 5.65. Var(X) = 5.65 - (2.05)^2 = 1.4475. Var(X/2) = 1/4Var(X) = 0.361875.

Applied Mathematics

Probability Distribution

Medium

applied

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

X 0 1 2 3 4
P(X) 0.1 0.25 0.3 0.2 0.15

Then, $\text{Var}\left(\frac{X}{2}\right)$ is :

X	0	1	2	3	4
P(X)	0.1	0.25	0.3	0.2	0.15

0.368751

0.361875

0.36758

0.369822

✅ Correct Option: 2

$E(X) = 0(0.1) + 1(0.25) + 2(0.3) + 3(0.2) + 4(0.15) = 2.05$ .

$E(X^2) = 0 + 0.25 + 1.2 + 1.8 + 2.4 = 5.65$ .

$\text{Var}(X) = 5.65 - (2.05)^2 = 1.4475$ .

$\text{Var}\left(\frac{X}{2}\right) = \frac{1}{4}\text{Var}(X) = 0.361875$ .

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	In a binomial distribution, if $n = 16$ , $p = 0.75$ , then the mean is	I.	$4$
B.	In a binomial distribution, if $n = 25$ , $p = \dfrac{1}{5}$ , then variance is	II.	$32$
C.	In a binomial distribution, the mean is 8 and the variance is 6, then the number of trials is	III.	$18$
D.	If the mean and variance of a binomial distribution are 6 and 4 respectively, then the number of trials is	IV.	$12$

Choose the correct answer from the options given below:

2026: 15 May Shift 1

A coin is tossed until a head appears, or the tail appears 4 times in succession, then the probability distribution of the number of tosses is

2026: 30 May Shift 2

There are 10% defective pens. In a sample of randomly selected 10 pens, the probability that atmost one pen is defective, is

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:

2023: 30 May Shift 3

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

The probability distribution of a random variable X is given below : X01234P(X)0.10.250.30.20.15 Then, Var(X2)\text{Var}\left(\frac{X}{2}\right)Var(2X​) is :

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CUET Mathematics Past Year Questions (Topic-Wise)

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

X 0 1 2 3 4
P(X) 0.1 0.25 0.3 0.2 0.15

Then, $\text{Var}\left(\frac{X}{2}\right)$ is :