A random variable X has the following probability distribution:, X, 0, 1, 2, 3, 4, P(X), 0.1, 0.15, 0.30, 0.30, 0.15, Which of the following are correct? (A) P(X ≤ 1)=0.25 (B) P(X>3)=0.15 (C) P(X=2)=0.30 (D) P(X ≤ 2)=0.55 Choose the correct answer from the options given below: Option 1: (A), (B) and (C) only Option 2: (A), (C) and (D) only Option 3: (B), (C) and (D) only Option 4: (A), (B), (C) and (D)

Answer: (A), (B), (C) and (D). Solution: (A) P(X≤1) = 0.1+0.15 = 0.25: correct. (B) P(X>3) = P(X=4) = 0.15: correct. (C) Read directly from the table as 0.30: correct. (D) P(X≤2) = 0.1+0.15+0.30 = 0.55: correct. All four statements hold.

Applied Mathematics

Probability Distribution

Easy

applied

A random variable X has the following probability distribution:

X 0 1 2 3 4
P(X) 0.1 0.15 0.30 0.30 0.15

Which of the following are correct?

(A) $P(X \le 1)=0.25$

(B) $P(X>3)=0.15$

(C) $P(X=2)=0.30$

(D) $P(X \le 2)=0.55$

Choose the correct answer from the options given below:

X	0	1	2	3	4
P(X)	0.1	0.15	0.30	0.30	0.15

(A), (B) and (C) only

(A), (C) and (D) only

(B), (C) and (D) only

(A), (B), (C) and (D)

✅ Correct Option: 4

(A) $P(X\le1) = 0.1+0.15 = 0.25$ : correct.

(B) $P(X>3) = P(X=4) = 0.15$ : correct.

(D) $P(X\le2) = 0.1+0.15+0.30 = 0.55$ : correct.

All four statements hold.

2026: 19 May Shift 2

The mean and variance of a Binomial distribution are 4 and 4/3 respectively. The number of trials is

2026: 15 May Shift 1

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

2026: 26 May Shift 2

In a random experiment, a collection of trials is called Bernoulli trials then which of the following statements are TRUE?

A. The number of trials is infinite.

B. Each trial has exactly two outcomes defined as success and failure.

C. The trials are dependent by nature.

D. The probability of success remains the same in each trial.

Choose the correct answer from the options given below:

2026: 25 May Shift 1

The mean and variance of a random variable $X$ having a binomial distribution are 1 and 2/3 respectively. Then,

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. $P(X=0)$	I. $1/27$
B. $P(X=3)$	II. $2/9$
C. $P(X=2)$	III. $4/9$
D. $P(X=1)$	IV. $8/27$

Choose the correct answer from the options given below:

2023: 15 June Shift 2

Match List - I with List - II.

List - I	List - II
(A) In a binomial distribution, if $n = 10$ , $q = 0.25$ , then its mean is	(I) 12
(B) If the mean of a binomial distribution is 6 and its variance is 3, then p is	(II) 7.5
(C) In a binomial distribution, the probability of getting a success is $\frac{1}{4}$ and the standard distribution is 3, then its mean is	(III) 16
(D) If the mean and variance of a binomial distribution are 4 and 3 respectively, then the number of trials is	(IV) $\frac{1}{2}$

Choose the correct answer from the options given below :

2026: 21 May Shift 2

A random variable X follows Poisson distribution. The variance of X is 2. The value of $P(X=3)$ is

Solution

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